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{text-align:center; } +table.gather {width:100%;} +div.gather-star {text-align:center;} +/* end css.sty */ + diff --git a/doc/html/mammult_doc.html b/doc/html/mammult_doc.html new file mode 100644 index 0000000..90054b6 --- /dev/null +++ b/doc/html/mammult_doc.html @@ -0,0 +1,307 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>MAMMULT: Metrics And Models for MULTilayer networks</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <div class="maketitle"> + + + + + + + + + + +<h2 class="titleHead">MAMMULT: Metrics And Models for MULTilayer +networks</h2> +<div class="author" ></div><br /> +<div class="date" ><span +class="cmr-12">19th</span><span +class="cmr-12"> October 2015</span></div> + + + + </div> + + + + <div class="tableofcontents"> + <span class="chapterToc" >1 <a +href="mammult_docch1.html#x2-10001" id="QQ2-2-1">Structural descriptors</a></span> +<br />  <span class="sectionToc" >1.1 <a +href="mammult_docse1.html#x3-20001.1" id="QQ2-3-2">Basic node, edge, and layer properties</a></span> +<br />   <span class="subsectionToc" >1.1.1 <a +href="mammult_docsu1.html#x4-30001.1.1" id="QQ2-4-3">Node and layer activity</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu2.html#x5-40001.1.1" id="QQ2-5-4"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_activity.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu3.html#x6-50001.1.1" id="QQ2-6-5"><span +class="cmtt-10x-x-109">layer</span><span +class="cmtt-10x-x-109">_activity.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu4.html#x7-60001.1.1" id="QQ2-7-6"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu5.html#x8-70001.1.1" id="QQ2-8-7"><span +class="cmtt-10x-x-109">layer</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu6.html#x9-80001.1.1" id="QQ2-9-8"><span +class="cmtt-10x-x-109">multiplexity.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu7.html#x10-90001.1.1" id="QQ2-10-9"><span +class="cmtt-10x-x-109">hamming</span><span +class="cmtt-10x-x-109">_dist.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu8.html#x11-100001.1.1" id="QQ2-11-10"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_degree</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu9.html#x12-110001.1.1" id="QQ2-12-11"><span +class="cmtt-10x-x-109">degs</span><span +class="cmtt-10x-x-109">_to</span><span +class="cmtt-10x-x-109">_binary.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu10.html#x13-120001.1.1" id="QQ2-13-12"><span +class="cmtt-10x-x-109">degs</span><span +class="cmtt-10x-x-109">_to</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> +<br />   <span class="subsectionToc" >1.1.2 <a +href="mammult_docsu11.html#x14-130001.1.2" id="QQ2-14-13">Layer aggregation</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu12.html#x15-140001.1.2" id="QQ2-15-14"><span +class="cmtt-10x-x-109">aggregate</span><span +class="cmtt-10x-x-109">_layers</span><span +class="cmtt-10x-x-109">_w.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu13.html#x16-150001.1.2" id="QQ2-16-15"><span +class="cmtt-10x-x-109">intersect</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> +<br />   <span class="subsectionToc" >1.1.3 <a +href="mammult_docsu14.html#x17-160001.1.3" id="QQ2-17-16">Node degree, participation coefficient, cartography</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu15.html#x18-170001.1.3" id="QQ2-18-17"><span +class="cmtt-10x-x-109">overlap</span><span +class="cmtt-10x-x-109">_degree.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu16.html#x19-180001.1.3" id="QQ2-19-18"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu17.html#x20-190001.1.3" id="QQ2-20-19"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_deg</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu18.html#x21-200001.1.3" id="QQ2-21-20"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_columns.py</span></a></span> +<br />   <span class="subsectionToc" >1.1.4 <a +href="mammult_docsu19.html#x22-210001.1.4" id="QQ2-22-21">Edge overlap, reinforcement</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu20.html#x23-220001.1.4" id="QQ2-23-22"><span +class="cmtt-10x-x-109">edge</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu21.html#x24-230001.1.4" id="QQ2-24-23"><span +class="cmtt-10x-x-109">avg</span><span +class="cmtt-10x-x-109">_edge</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu22.html#x25-240001.1.4" id="QQ2-25-24"><span +class="cmtt-10x-x-109">reinforcement.py</span></a></span> +<br />  <span class="sectionToc" >1.2 <a +href="mammult_docse2.html#x26-250001.2" id="QQ2-26-25">Inter-layer degree correlations</a></span> +<br />   <span class="subsectionToc" >1.2.1 <a +href="mammult_docsu23.html#x27-260001.2.1" id="QQ2-27-26">Node ranking</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu24.html#x28-270001.2.1" id="QQ2-28-27"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_nodes.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu25.html#x29-280001.2.1" id="QQ2-29-28"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_nodes</span><span +class="cmtt-10x-x-109">_thresh.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu26.html#x30-290001.2.1" id="QQ2-30-29"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_occurrence.py</span></a></span> +<br />   <span class="subsectionToc" >1.2.2 <a +href="mammult_docsu27.html#x31-300001.2.2" id="QQ2-31-30">Interlayer degree correlation coefficients</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu28.html#x32-310001.2.2" id="QQ2-32-31"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_pearson.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu29.html#x33-320001.2.2" id="QQ2-33-32"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_rho.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu30.html#x34-330001.2.2" id="QQ2-34-33"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_tau.py</span></a></span> +<br />   <span class="subsectionToc" >1.2.3 <a +href="mammult_docsu31.html#x35-340001.2.3" id="QQ2-35-34">Interlayer degree correlation functions</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu32.html#x36-350001.2.3" id="QQ2-36-35"><span +class="cmtt-10x-x-109">dump</span><span +class="cmtt-10x-x-109">_k</span><span +class="cmtt-10x-x-109">_q</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu33.html#x37-360001.2.3" id="QQ2-37-36"><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu34.html#x38-370001.2.3" id="QQ2-38-37"><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_degrees.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu35.html#x39-380001.2.3" id="QQ2-39-38"><span +class="cmtt-10x-x-109">fit</span><span +class="cmtt-10x-x-109">_knn</span></a></span> +<br /> <span class="chapterToc" >2 <a +href="mammult_docch2.html#x40-390002" id="QQ2-40-39">Models of multi-layer networks</a></span> +<br />  <span class="sectionToc" >2.1 <a +href="mammult_docse3.html#x41-400002.1" id="QQ2-41-40">Null models</a></span> +<br />   <span class="subsectionToc" >2.1.1 <a +href="mammult_docsu36.html#x42-410002.1.1" id="QQ2-42-41">Null-models of node and layer activity</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu37.html#x43-420002.1.1" id="QQ2-43-42"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_hypergeometric.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu38.html#x44-430002.1.1" id="QQ2-44-43"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_MDM.py</span></a></span> + + + +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu39.html#x45-440002.1.1" id="QQ2-45-44"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_MSM.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu40.html#x46-450002.1.1" id="QQ2-46-45"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_layer</span><span +class="cmtt-10x-x-109">_growth.py</span></a></span> +<br />  <span class="sectionToc" >2.2 <a +href="mammult_docse4.html#x47-460002.2" id="QQ2-47-46">Growing multiplex networks</a></span> +<br />   <span class="subsectionToc" >2.2.1 <a +href="mammult_docsu41.html#x48-470002.2.1" id="QQ2-48-47">Linear preferential attachment</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu42.html#x49-480002.2.1" id="QQ2-49-48"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delta</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu43.html#x50-490002.2.1" id="QQ2-50-49"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delay</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu44.html#x51-500002.2.1" id="QQ2-51-50"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delay</span><span +class="cmtt-10x-x-109">_mix</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu45.html#x52-510002.2.1" id="QQ2-52-51"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_random</span><span +class="cmtt-10x-x-109">_times</span></a></span> +<br />   <span class="subsectionToc" >2.2.2 <a +href="mammult_docsu46.html#x53-520002.2.2" id="QQ2-53-52">Non-linear preferential attachment</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu47.html#x54-530002.2.2" id="QQ2-54-53"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_nonlinear</span></a></span> +<br />   <span class="subsectionToc" >2.2.3 <a +href="mammult_docsu48.html#x55-540002.2.3" id="QQ2-55-54">Utilities</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu49.html#x56-550002.2.3" id="QQ2-56-55"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_deg</span><span +class="cmtt-10x-x-109">_over</span><span +class="cmtt-10x-x-109">_time.py</span></a></span> +<br />  <span class="sectionToc" >2.3 <a +href="mammult_docse5.html#x57-560002.3" id="QQ2-57-56">Multiplex networks with inter-layer degree correlations</a></span> +<br />   <span class="subsectionToc" >2.3.1 <a +href="mammult_docsu50.html#x58-570002.3.1" id="QQ2-58-57">Models based on simulated annealing</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu51.html#x59-580002.3.1" id="QQ2-59-58"><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_rho</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu52.html#x60-590002.3.1" id="QQ2-60-59"><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_qnn</span><span +class="cmtt-10x-x-109">_adaptive</span></a></span> +<br /> <span class="chapterToc" >3 <a +href="mammult_docch3.html#x61-600003" id="QQ2-61-60">Dynamics on multi-layer networks</a></span> +<br />  <span class="sectionToc" >3.1 <a +href="mammult_docse6.html#x62-610003.1" id="QQ2-62-61">Interacting opinions - Multilayer ising model</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu53.html#x63-620003.1" id="QQ2-63-62"><span +class="cmtt-10x-x-109">multiplex</span><span +class="cmtt-10x-x-109">_ising</span></a></span> +<br />  <span class="sectionToc" >3.2 <a +href="mammult_docse7.html#x64-630003.2" id="QQ2-64-63">Biased random walks</a></span> +<br />   <span class="subsectionToc" >3.2.1 <a +href="mammult_docsu54.html#x65-640003.2.1" id="QQ2-65-64">Stationary distribution</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu55.html#x66-650003.2.1" id="QQ2-66-65"><span +class="cmtt-10x-x-109">statdistr2</span></a></span> +<br />   <span class="subsectionToc" >3.2.2 <a +href="mammult_docsu56.html#x67-660003.2.2" id="QQ2-67-66">Entropy rate</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu57.html#x68-670003.2.2" id="QQ2-68-67"><span +class="cmtt-10x-x-109">entropyrate2add</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu58.html#x69-680003.2.2" id="QQ2-69-68"><span +class="cmtt-10x-x-109">entropyrate2mult</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu59.html#x70-690003.2.2" id="QQ2-70-69"><span +class="cmtt-10x-x-109">entropyrate2int</span></a></span> + </div> + + + + + + + + +<!--l. 265--><p class="noindent" ><span class="next">[<a +href="mammult_docch1.html" id="tailmammult_doc" >next</a>]</span> +</body></html> + + + + diff --git a/doc/html/mammult_doc0x.png b/doc/html/mammult_doc0x.png Binary files differnew file mode 100644 index 0000000..a20f1b7 --- /dev/null +++ b/doc/html/mammult_doc0x.png diff --git a/doc/html/mammult_doc10x.png b/doc/html/mammult_doc10x.png Binary files differnew file mode 100644 index 0000000..5f94b17 --- /dev/null +++ b/doc/html/mammult_doc10x.png diff --git a/doc/html/mammult_doc11x.png b/doc/html/mammult_doc11x.png Binary files differnew file mode 100644 index 0000000..775dead --- /dev/null +++ b/doc/html/mammult_doc11x.png diff --git a/doc/html/mammult_doc12x.png b/doc/html/mammult_doc12x.png Binary files differnew file mode 100644 index 0000000..475dd5c --- /dev/null +++ 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+++ b/doc/html/mammult_doc8x.png diff --git a/doc/html/mammult_doc9x.png b/doc/html/mammult_doc9x.png Binary files differnew file mode 100644 index 0000000..8562067 --- /dev/null +++ b/doc/html/mammult_doc9x.png diff --git a/doc/html/mammult_docch1.html b/doc/html/mammult_docch1.html new file mode 100644 index 0000000..d9f664b --- /dev/null +++ b/doc/html/mammult_docch1.html @@ -0,0 +1,57 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1 Structural descriptors</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 125--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse1.html" >next</a>] [<a +href="mammult_doc.html" >prev</a>] [<a +href="mammult_doc.html#tailmammult_doc" >prev-tail</a>] [<a +href="#tailmammult_docch1.html">tail</a>] [<a +href="mammult_doc.html#mammult_docch1.html" >up</a>] </p></div> + <h2 class="chapterHead"><span class="titlemark">Chapter 1</span><br /><a + id="x2-10001"></a>Structural descriptors</h2> + <div class="sectionTOCS"> +  <span class="sectionToc" >1.1 <a +href="mammult_docse1.html#x3-20001.1">Basic node, edge, and layer properties</a></span> +<br />   <span class="subsectionToc" >1.1.1 <a +href="mammult_docsu1.html#x4-30001.1.1">Node and layer activity</a></span> +<br />   <span class="subsectionToc" >1.1.2 <a +href="mammult_docsu11.html#x14-130001.1.2">Layer aggregation</a></span> +<br />   <span class="subsectionToc" >1.1.3 <a +href="mammult_docsu14.html#x17-160001.1.3">Node degree, participation coefficient, cartography</a></span> +<br />   <span class="subsectionToc" >1.1.4 <a +href="mammult_docsu19.html#x22-210001.1.4">Edge overlap, reinforcement</a></span> +<br />  <span class="sectionToc" >1.2 <a +href="mammult_docse2.html#x26-250001.2">Inter-layer degree correlations</a></span> +<br />   <span class="subsectionToc" >1.2.1 <a +href="mammult_docsu23.html#x27-260001.2.1">Node ranking</a></span> +<br />   <span class="subsectionToc" >1.2.2 <a +href="mammult_docsu27.html#x31-300001.2.2">Interlayer degree correlation coefficients</a></span> +<br />   <span class="subsectionToc" >1.2.3 <a +href="mammult_docsu31.html#x35-340001.2.3">Interlayer degree correlation functions</a></span> + + + + </div> + + + + + <!--l. 208--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse1.html" >next</a>] [<a +href="mammult_doc.html" >prev</a>] [<a +href="mammult_doc.html#tailmammult_doc" >prev-tail</a>] [<a +href="mammult_docch1.html" >front</a>] [<a +href="mammult_doc.html#mammult_docch1.html" >up</a>] </p></div> +<!--l. 208--><p class="indent" > <a + id="tailmammult_docch1.html"></a> +</body></html> diff --git a/doc/html/mammult_docch2.html b/doc/html/mammult_docch2.html new file mode 100644 index 0000000..2d7be08 --- /dev/null +++ b/doc/html/mammult_docch2.html @@ -0,0 +1,53 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2 Models of multi-layer networks</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 208--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse3.html" >next</a>] [<a +href="mammult_docsu35.html" >prev</a>] [<a +href="mammult_docsu35.html#tailmammult_docsu35.html" >prev-tail</a>] [<a +href="#tailmammult_docch2.html">tail</a>] [<a +href="mammult_doc.html#mammult_docch2.html" >up</a>] </p></div> + <h2 class="chapterHead"><span class="titlemark">Chapter 2</span><br /><a + id="x40-390002"></a>Models of multi-layer networks</h2> + <div class="sectionTOCS"> +  <span class="sectionToc" >2.1 <a +href="mammult_docse3.html#x41-400002.1">Null models</a></span> +<br />   <span class="subsectionToc" >2.1.1 <a +href="mammult_docsu36.html#x42-410002.1.1">Null-models of node and layer activity</a></span> +<br />  <span class="sectionToc" >2.2 <a +href="mammult_docse4.html#x47-460002.2">Growing multiplex networks</a></span> +<br />   <span class="subsectionToc" >2.2.1 <a +href="mammult_docsu41.html#x48-470002.2.1">Linear preferential attachment</a></span> +<br />   <span class="subsectionToc" >2.2.2 <a +href="mammult_docsu46.html#x53-520002.2.2">Non-linear preferential attachment</a></span> +<br />   <span class="subsectionToc" >2.2.3 <a +href="mammult_docsu48.html#x55-540002.2.3">Utilities</a></span> +<br />  <span class="sectionToc" >2.3 <a +href="mammult_docse5.html#x57-560002.3">Multiplex networks with inter-layer degree correlations</a></span> +<br />   <span class="subsectionToc" >2.3.1 <a +href="mammult_docsu50.html#x58-570002.3.1">Models based on simulated annealing</a></span> + </div> + + + + + + <!--l. 247--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse3.html" >next</a>] [<a +href="mammult_docsu35.html" >prev</a>] [<a +href="mammult_docsu35.html#tailmammult_docsu35.html" >prev-tail</a>] [<a +href="mammult_docch2.html" >front</a>] [<a +href="mammult_doc.html#mammult_docch2.html" >up</a>] </p></div> +<!--l. 247--><p class="indent" > <a + id="tailmammult_docch2.html"></a> +</body></html> diff --git a/doc/html/mammult_docch3.html b/doc/html/mammult_docch3.html new file mode 100644 index 0000000..e392f28 --- /dev/null +++ b/doc/html/mammult_docch3.html @@ -0,0 +1,44 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>3 Dynamics on multi-layer networks</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 247--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse6.html" >next</a>] [<a +href="mammult_docsu52.html" >prev</a>] [<a +href="mammult_docsu52.html#tailmammult_docsu52.html" >prev-tail</a>] [<a +href="#tailmammult_docch3.html">tail</a>] [<a +href="mammult_doc.html#mammult_docch3.html" >up</a>] </p></div> + <h2 class="chapterHead"><span class="titlemark">Chapter 3</span><br /><a + id="x61-600003"></a>Dynamics on multi-layer networks</h2> + <div class="sectionTOCS"> +  <span class="sectionToc" >3.1 <a +href="mammult_docse6.html#x62-610003.1">Interacting opinions - Multilayer ising model</a></span> +<br />  <span class="sectionToc" >3.2 <a +href="mammult_docse7.html#x64-630003.2">Biased random walks</a></span> +<br />   <span class="subsectionToc" >3.2.1 <a +href="mammult_docsu54.html#x65-640003.2.1">Stationary distribution</a></span> +<br />   <span class="subsectionToc" >3.2.2 <a +href="mammult_docsu56.html#x67-660003.2.2">Entropy rate</a></span> + </div> + + + + + <!--l. 265--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse6.html" >next</a>] [<a +href="mammult_docsu52.html" >prev</a>] [<a +href="mammult_docsu52.html#tailmammult_docsu52.html" >prev-tail</a>] [<a +href="mammult_docch3.html" >front</a>] [<a +href="mammult_doc.html#mammult_docch3.html" >up</a>] </p></div> +<!--l. 265--><p class="indent" > <a + id="tailmammult_docch3.html"></a> +</body></html> diff --git a/doc/html/mammult_docse1.html b/doc/html/mammult_docse1.html new file mode 100644 index 0000000..776bf28 --- /dev/null +++ b/doc/html/mammult_docse1.html @@ -0,0 +1,129 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Basic node, edge, and layer properties</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 127--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu1.html" >next</a>] [<a +href="mammult_docch1.html" >prev</a>] [<a +href="mammult_docch1.html#tailmammult_docch1.html" >prev-tail</a>] [<a +href="#tailmammult_docse1.html">tail</a>] [<a +href="mammult_docch1.html#mammult_docse1.html" >up</a>] </p></div> + <h3 class="sectionHead"><span class="titlemark">1.1 </span> <a + id="x3-20001.1"></a>Basic node, edge, and layer properties</h3> +<!--l. 129--><p class="noindent" > + <div class="subsectionTOCS"> +   <span class="subsectionToc" >1.1.1 <a +href="mammult_docsu1.html#x4-30001.1.1">Node and layer activity</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu2.html#x5-40001.1.1"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_activity.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu3.html#x6-50001.1.1"><span +class="cmtt-10x-x-109">layer</span><span +class="cmtt-10x-x-109">_activity.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu4.html#x7-60001.1.1"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu5.html#x8-70001.1.1"><span +class="cmtt-10x-x-109">layer</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu6.html#x9-80001.1.1"><span +class="cmtt-10x-x-109">multiplexity.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu7.html#x10-90001.1.1"><span +class="cmtt-10x-x-109">hamming</span><span +class="cmtt-10x-x-109">_dist.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu8.html#x11-100001.1.1"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_degree</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu9.html#x12-110001.1.1"><span +class="cmtt-10x-x-109">degs</span><span +class="cmtt-10x-x-109">_to</span><span +class="cmtt-10x-x-109">_binary.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu10.html#x13-120001.1.1"><span +class="cmtt-10x-x-109">degs</span><span +class="cmtt-10x-x-109">_to</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> +<br />   <span class="subsectionToc" >1.1.2 <a +href="mammult_docsu11.html#x14-130001.1.2">Layer aggregation</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu12.html#x15-140001.1.2"><span +class="cmtt-10x-x-109">aggregate</span><span +class="cmtt-10x-x-109">_layers</span><span +class="cmtt-10x-x-109">_w.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu13.html#x16-150001.1.2"><span +class="cmtt-10x-x-109">intersect</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> +<br />   <span class="subsectionToc" >1.1.3 <a +href="mammult_docsu14.html#x17-160001.1.3">Node degree, participation coefficient, cartography</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu15.html#x18-170001.1.3"><span +class="cmtt-10x-x-109">overlap</span><span +class="cmtt-10x-x-109">_degree.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu16.html#x19-180001.1.3"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu17.html#x20-190001.1.3"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_deg</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu18.html#x21-200001.1.3"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_columns.py</span></a></span> +<br />   <span class="subsectionToc" >1.1.4 <a +href="mammult_docsu19.html#x22-210001.1.4">Edge overlap, reinforcement</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu20.html#x23-220001.1.4"><span +class="cmtt-10x-x-109">edge</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu21.html#x24-230001.1.4"><span +class="cmtt-10x-x-109">avg</span><span +class="cmtt-10x-x-109">_edge</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu22.html#x25-240001.1.4"><span +class="cmtt-10x-x-109">reinforcement.py</span></a></span> + </div> + + + + + + + <!--l. 172--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu1.html" >next</a>] [<a +href="mammult_docch1.html" >prev</a>] [<a +href="mammult_docch1.html#tailmammult_docch1.html" >prev-tail</a>] [<a +href="mammult_docse1.html" >front</a>] [<a +href="mammult_docch1.html#mammult_docse1.html" >up</a>] </p></div> +<!--l. 172--><p class="indent" > <a + id="tailmammult_docse1.html"></a> +</body></html> diff --git a/doc/html/mammult_docse2.html b/doc/html/mammult_docse2.html new file mode 100644 index 0000000..deb5077 --- /dev/null +++ b/doc/html/mammult_docse2.html @@ -0,0 +1,90 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Inter-layer degree correlations</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 172--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu23.html" >next</a>] [<a +href="mammult_docsu22.html" >prev</a>] [<a +href="mammult_docsu22.html#tailmammult_docsu22.html" >prev-tail</a>] [<a +href="#tailmammult_docse2.html">tail</a>] [<a +href="mammult_docch1.html#mammult_docse2.html" >up</a>] </p></div> + <h3 class="sectionHead"><span class="titlemark">1.2 </span> <a + id="x26-250001.2"></a>Inter-layer degree correlations</h3> +<!--l. 174--><p class="noindent" > + <div class="subsectionTOCS"> +   <span class="subsectionToc" >1.2.1 <a +href="mammult_docsu23.html#x27-260001.2.1">Node ranking</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu24.html#x28-270001.2.1"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_nodes.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu25.html#x29-280001.2.1"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_nodes</span><span +class="cmtt-10x-x-109">_thresh.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu26.html#x30-290001.2.1"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_occurrence.py</span></a></span> +<br />   <span class="subsectionToc" >1.2.2 <a +href="mammult_docsu27.html#x31-300001.2.2">Interlayer degree correlation coefficients</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu28.html#x32-310001.2.2"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_pearson.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu29.html#x33-320001.2.2"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_rho.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu30.html#x34-330001.2.2"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_tau.py</span></a></span> +<br />   <span class="subsectionToc" >1.2.3 <a +href="mammult_docsu31.html#x35-340001.2.3">Interlayer degree correlation functions</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu32.html#x36-350001.2.3"><span +class="cmtt-10x-x-109">dump</span><span +class="cmtt-10x-x-109">_k</span><span +class="cmtt-10x-x-109">_q</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu33.html#x37-360001.2.3"><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu34.html#x38-370001.2.3"><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_degrees.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu35.html#x39-380001.2.3"><span +class="cmtt-10x-x-109">fit</span><span +class="cmtt-10x-x-109">_knn</span></a></span> + </div> + + + + + + <!--l. 208--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu23.html" >next</a>] [<a +href="mammult_docsu22.html" >prev</a>] [<a +href="mammult_docsu22.html#tailmammult_docsu22.html" >prev-tail</a>] [<a +href="mammult_docse2.html" >front</a>] [<a +href="mammult_docch1.html#mammult_docse2.html" >up</a>] </p></div> +<!--l. 208--><p class="indent" > <a + id="tailmammult_docse2.html"></a> +</body></html> diff --git a/doc/html/mammult_docse3.html b/doc/html/mammult_docse3.html new file mode 100644 index 0000000..f05a21a --- /dev/null +++ b/doc/html/mammult_docse3.html @@ -0,0 +1,55 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Null models</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 210--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu36.html" >next</a>] [<a +href="mammult_docch2.html" >prev</a>] [<a +href="mammult_docch2.html#tailmammult_docch2.html" >prev-tail</a>] [<a +href="#tailmammult_docse3.html">tail</a>] [<a +href="mammult_docch2.html#mammult_docse3.html" >up</a>] </p></div> + <h3 class="sectionHead"><span class="titlemark">2.1 </span> <a + id="x41-400002.1"></a>Null models</h3> +<!--l. 212--><p class="noindent" > + <div class="subsectionTOCS"> +   <span class="subsectionToc" >2.1.1 <a +href="mammult_docsu36.html#x42-410002.1.1">Null-models of node and layer activity</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu37.html#x43-420002.1.1"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_hypergeometric.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu38.html#x44-430002.1.1"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_MDM.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu39.html#x45-440002.1.1"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_MSM.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu40.html#x46-450002.1.1"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_layer</span><span +class="cmtt-10x-x-109">_growth.py</span></a></span> + </div> + + + + <!--l. 220--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu36.html" >next</a>] [<a +href="mammult_docch2.html" >prev</a>] [<a +href="mammult_docch2.html#tailmammult_docch2.html" >prev-tail</a>] [<a +href="mammult_docse3.html" >front</a>] [<a +href="mammult_docch2.html#mammult_docse3.html" >up</a>] </p></div> +<!--l. 220--><p class="indent" > <a + id="tailmammult_docse3.html"></a> +</body></html> diff --git a/doc/html/mammult_docse4.html b/doc/html/mammult_docse4.html new file mode 100644 index 0000000..2ab68dd --- /dev/null +++ b/doc/html/mammult_docse4.html @@ -0,0 +1,76 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Growing multiplex networks</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 220--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu41.html" >next</a>] [<a +href="mammult_docsu40.html" >prev</a>] [<a +href="mammult_docsu40.html#tailmammult_docsu40.html" >prev-tail</a>] [<a +href="#tailmammult_docse4.html">tail</a>] [<a +href="mammult_docch2.html#mammult_docse4.html" >up</a>] </p></div> + <h3 class="sectionHead"><span class="titlemark">2.2 </span> <a + id="x47-460002.2"></a>Growing multiplex networks</h3> +<!--l. 222--><p class="noindent" > + <div class="subsectionTOCS"> +   <span class="subsectionToc" >2.2.1 <a +href="mammult_docsu41.html#x48-470002.2.1">Linear preferential attachment</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu42.html#x49-480002.2.1"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delta</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu43.html#x50-490002.2.1"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delay</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu44.html#x51-500002.2.1"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delay</span><span +class="cmtt-10x-x-109">_mix</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu45.html#x52-510002.2.1"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_random</span><span +class="cmtt-10x-x-109">_times</span></a></span> +<br />   <span class="subsectionToc" >2.2.2 <a +href="mammult_docsu46.html#x53-520002.2.2">Non-linear preferential attachment</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu47.html#x54-530002.2.2"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_nonlinear</span></a></span> +<br />   <span class="subsectionToc" >2.2.3 <a +href="mammult_docsu48.html#x55-540002.2.3">Utilities</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu49.html#x56-550002.2.3"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_deg</span><span +class="cmtt-10x-x-109">_over</span><span +class="cmtt-10x-x-109">_time.py</span></a></span> + </div> + + + + + + <!--l. 239--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu41.html" >next</a>] [<a +href="mammult_docsu40.html" >prev</a>] [<a +href="mammult_docsu40.html#tailmammult_docsu40.html" >prev-tail</a>] [<a +href="mammult_docse4.html" >front</a>] [<a +href="mammult_docch2.html#mammult_docse4.html" >up</a>] </p></div> +<!--l. 239--><p class="indent" > <a + id="tailmammult_docse4.html"></a> +</body></html> diff --git a/doc/html/mammult_docse5.html b/doc/html/mammult_docse5.html new file mode 100644 index 0000000..44ac716 --- /dev/null +++ b/doc/html/mammult_docse5.html @@ -0,0 +1,47 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Multiplex networks with inter-layer degree correlations</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 239--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu50.html" >next</a>] [<a +href="mammult_docsu49.html" >prev</a>] [<a +href="mammult_docsu49.html#tailmammult_docsu49.html" >prev-tail</a>] [<a +href="#tailmammult_docse5.html">tail</a>] [<a +href="mammult_docch2.html#mammult_docse5.html" >up</a>] </p></div> + <h3 class="sectionHead"><span class="titlemark">2.3 </span> <a + id="x57-560002.3"></a>Multiplex networks with inter-layer degree correlations</h3> +<!--l. 241--><p class="noindent" > + <div class="subsectionTOCS"> +   <span class="subsectionToc" >2.3.1 <a +href="mammult_docsu50.html#x58-570002.3.1">Models based on simulated annealing</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu51.html#x59-580002.3.1"><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_rho</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu52.html#x60-590002.3.1"><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_qnn</span><span +class="cmtt-10x-x-109">_adaptive</span></a></span> + </div> + + + + <!--l. 247--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu50.html" >next</a>] [<a +href="mammult_docsu49.html" >prev</a>] [<a +href="mammult_docsu49.html#tailmammult_docsu49.html" >prev-tail</a>] [<a +href="mammult_docse5.html" >front</a>] [<a +href="mammult_docch2.html#mammult_docse5.html" >up</a>] </p></div> +<!--l. 247--><p class="indent" > <a + id="tailmammult_docse5.html"></a> +</body></html> diff --git a/doc/html/mammult_docse6.html b/doc/html/mammult_docse6.html new file mode 100644 index 0000000..fab8160 --- /dev/null +++ b/doc/html/mammult_docse6.html @@ -0,0 +1,40 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Interacting opinions - Multilayer ising model</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 249--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu53.html" >next</a>] [<a +href="mammult_docch3.html" >prev</a>] [<a +href="mammult_docch3.html#tailmammult_docch3.html" >prev-tail</a>] [<a +href="#tailmammult_docse6.html">tail</a>] [<a +href="mammult_docch3.html#mammult_docse6.html" >up</a>] </p></div> + <h3 class="sectionHead"><span class="titlemark">3.1 </span> <a + id="x62-610003.1"></a>Interacting opinions - Multilayer ising model</h3> +<!--l. 7--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu53.html#x63-620003.1"><span +class="cmtt-10x-x-109">multiplex</span><span +class="cmtt-10x-x-109">_ising</span></a></span> + </div> + + + + <!--l. 253--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu53.html" >next</a>] [<a +href="mammult_docch3.html" >prev</a>] [<a +href="mammult_docch3.html#tailmammult_docch3.html" >prev-tail</a>] [<a +href="mammult_docse6.html" >front</a>] [<a +href="mammult_docch3.html#mammult_docse6.html" >up</a>] </p></div> +<!--l. 253--><p class="indent" > <a + id="tailmammult_docse6.html"></a> +</body></html> diff --git a/doc/html/mammult_docse7.html b/doc/html/mammult_docse7.html new file mode 100644 index 0000000..89e367b --- /dev/null +++ b/doc/html/mammult_docse7.html @@ -0,0 +1,49 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Biased random walks</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 253--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu54.html" >next</a>] [<a +href="mammult_docsu53.html" >prev</a>] [<a +href="mammult_docsu53.html#tailmammult_docsu53.html" >prev-tail</a>] [<a +href="#tailmammult_docse7.html">tail</a>] [<a +href="mammult_docch3.html#mammult_docse7.html" >up</a>] </p></div> + <h3 class="sectionHead"><span class="titlemark">3.2 </span> <a + id="x64-630003.2"></a>Biased random walks</h3> +<!--l. 255--><p class="noindent" > + <div class="subsectionTOCS"> +   <span class="subsectionToc" >3.2.1 <a +href="mammult_docsu54.html#x65-640003.2.1">Stationary distribution</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu55.html#x66-650003.2.1"><span +class="cmtt-10x-x-109">statdistr2</span></a></span> +<br />   <span class="subsectionToc" >3.2.2 <a +href="mammult_docsu56.html#x67-660003.2.2">Entropy rate</a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu57.html#x68-670003.2.2"><span +class="cmtt-10x-x-109">entropyrate2add</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu58.html#x69-680003.2.2"><span +class="cmtt-10x-x-109">entropyrate2mult</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu59.html#x70-690003.2.2"><span +class="cmtt-10x-x-109">entropyrate2int</span></a></span> + </div> +<!--l. 265--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu54.html" >next</a>] [<a +href="mammult_docsu53.html" >prev</a>] [<a +href="mammult_docsu53.html#tailmammult_docsu53.html" >prev-tail</a>] [<a +href="mammult_docse7.html" >front</a>] [<a +href="mammult_docch3.html#mammult_docse7.html" >up</a>] </p></div> +<!--l. 265--><p class="indent" > <a + id="tailmammult_docse7.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu1.html b/doc/html/mammult_docsu1.html new file mode 100644 index 0000000..6790cf6 --- /dev/null +++ b/doc/html/mammult_docsu1.html @@ -0,0 +1,91 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Node and layer activity</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 129--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu2.html" >next</a>] [<a +href="mammult_docse1.html" >prev</a>] [<a +href="mammult_docse1.html#tailmammult_docse1.html" >prev-tail</a>] [<a +href="#tailmammult_docsu1.html">tail</a>] [<a +href="mammult_docse1.html#mammult_docsu1.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">1.1.1 </span> <a + id="x4-30001.1.1"></a>Node and layer activity</h4> +<!--l. 131--><p class="noindent" >This section includes programs related to the computation of node and layer +activity, activity vectors, pairwise multiplexity, pairwise normalised Hamming +distance, node degree vectors. +<!--l. 7--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu2.html#x5-40001.1.1"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_activity.py</span></a></span> + + + +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu3.html#x6-50001.1.1"><span +class="cmtt-10x-x-109">layer</span><span +class="cmtt-10x-x-109">_activity.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu4.html#x7-60001.1.1"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu5.html#x8-70001.1.1"><span +class="cmtt-10x-x-109">layer</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu6.html#x9-80001.1.1"><span +class="cmtt-10x-x-109">multiplexity.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu7.html#x10-90001.1.1"><span +class="cmtt-10x-x-109">hamming</span><span +class="cmtt-10x-x-109">_dist.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu8.html#x11-100001.1.1"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_degree</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu9.html#x12-110001.1.1"><span +class="cmtt-10x-x-109">degs</span><span +class="cmtt-10x-x-109">_to</span><span +class="cmtt-10x-x-109">_binary.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu10.html#x13-120001.1.1"><span +class="cmtt-10x-x-109">degs</span><span +class="cmtt-10x-x-109">_to</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> + </div> + + + + + + + + + + + + <!--l. 145--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu2.html" >next</a>] [<a +href="mammult_docse1.html" >prev</a>] [<a +href="mammult_docse1.html#tailmammult_docse1.html" >prev-tail</a>] [<a +href="mammult_docsu1.html" >front</a>] [<a +href="mammult_docse1.html#mammult_docsu1.html" >up</a>] </p></div> +<!--l. 145--><p class="indent" > <a + id="tailmammult_docsu1.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu10.html b/doc/html/mammult_docsu10.html new file mode 100644 index 0000000..99c1c17 --- /dev/null +++ b/doc/html/mammult_docsu10.html @@ -0,0 +1,97 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 degs_to_activity_overlap.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu11.html" >next</a>] [<a +href="mammult_docsu9.html" >prev</a>] [<a +href="mammult_docsu9.html#tailmammult_docsu9.html" >prev-tail</a>] [<a +href="#tailmammult_docsu10.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu10.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x13-120001.1.1"></a><span +class="cmtt-10x-x-109">degs</span><span +class="cmtt-10x-x-109">_to</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_overlap.py</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">degs</span><span +class="cmbx-10x-x-109">_to</span><span +class="cmbx-10x-x-109">_activity</span><span +class="cmbx-10x-x-109">_overlap.py </span>- compute the activity and the total +(overlapping) degree of all the nodes of a multiplex. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">degs</span><span +class="cmbx-10x-x-109">_to</span><span +class="cmbx-10x-x-109">_activity</span><span +class="cmbx-10x-x-109">_overlap.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">degree</span><span +class="cmitt-10x-x-109">_vectors</span><span +class="cmmi-10x-x-109">></span> +<!--l. 14--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 14--><p class="indent" > Take a file which contains, on the n-th line, the degrees at each layer of the +n-th node, (e.g., the result of the script <span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_degree</span><span +class="cmtt-10x-x-109">_vectors.py</span>), in the +format: +<!--l. 14--><p class="indent" >   <span +class="cmti-10x-x-109">noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_lay1 noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_lay2 ... noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_layM</span> +<!--l. 14--><p class="noindent" >and compute the activity (i.e., the number of layers in which a node is not +isolated) and the total (overlapping) degree of each node. +<!--l. 26--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 26--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains the +activity and the total degree of the n-th nodem in the format: +<!--l. 26--><p class="indent" >   <span +class="cmti-10x-x-109">noden</span><span +class="cmti-10x-x-109">_activity noden</span><span +class="cmti-10x-x-109">_tot</span><span +class="cmti-10x-x-109">_deg</span> +<!--l. 26--><p class="noindent" >As usual, the program assumes that node IDs start from zero and proceed +sequentially, without gaps, i.e., if a node ID is not present in any of the layer +files given as input, the program considers it as being isolated on all the +layers. +<!--l. 28--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 28--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 28--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 145--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu11.html" >next</a>] [<a +href="mammult_docsu9.html" >prev</a>] [<a +href="mammult_docsu9.html#tailmammult_docsu9.html" >prev-tail</a>] [<a +href="mammult_docsu10.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu10.html" >up</a>] </p></div> +<!--l. 145--><p class="indent" > <a + id="tailmammult_docsu10.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu11.html b/doc/html/mammult_docsu11.html new file mode 100644 index 0000000..af6ef30 --- /dev/null +++ b/doc/html/mammult_docsu11.html @@ -0,0 +1,48 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Layer aggregation</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 145--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu12.html" >next</a>] [<a +href="mammult_docsu10.html" >prev</a>] [<a +href="mammult_docsu10.html#tailmammult_docsu10.html" >prev-tail</a>] [<a +href="#tailmammult_docsu11.html">tail</a>] [<a +href="mammult_docse1.html#mammult_docsu11.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">1.1.2 </span> <a + id="x14-130001.1.2"></a>Layer aggregation</h4> +<!--l. 147--><p class="noindent" >This section includes programs to obtain various single-layer aggregated graphs +associated to a multiplex network. +<!--l. 3--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu12.html#x15-140001.1.2"><span +class="cmtt-10x-x-109">aggregate</span><span +class="cmtt-10x-x-109">_layers</span><span +class="cmtt-10x-x-109">_w.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu13.html#x16-150001.1.2"><span +class="cmtt-10x-x-109">intersect</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> + </div> + + + + + <!--l. 153--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu12.html" >next</a>] [<a +href="mammult_docsu10.html" >prev</a>] [<a +href="mammult_docsu10.html#tailmammult_docsu10.html" >prev-tail</a>] [<a +href="mammult_docsu11.html" >front</a>] [<a +href="mammult_docse1.html#mammult_docsu11.html" >up</a>] </p></div> +<!--l. 153--><p class="indent" > <a + id="tailmammult_docsu11.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu12.html b/doc/html/mammult_docsu12.html new file mode 100644 index 0000000..2d99541 --- /dev/null +++ b/doc/html/mammult_docsu12.html @@ -0,0 +1,104 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.2.0 aggregate_layers_w.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu13.html" >next</a>] [<a +href="mammult_docsu11.html" >prev</a>] [<a +href="mammult_docsu11.html#tailmammult_docsu11.html" >prev-tail</a>] [<a +href="#tailmammult_docsu12.html">tail</a>] [<a +href="mammult_docsu11.html#mammult_docsu12.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x15-140001.1.2"></a><span +class="cmtt-10x-x-109">aggregate</span><span +class="cmtt-10x-x-109">_layers</span><span +class="cmtt-10x-x-109">_w.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">aggregate</span><span +class="cmbx-10x-x-109">_layers</span><span +class="cmbx-10x-x-109">_w.py </span>- compute the (weighted) aggregated graph +associated to a multiplex. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">aggregate</span><span +class="cmbx-10x-x-109">_layers</span><span +class="cmbx-10x-x-109">_w.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer3</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 17--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 17--><p class="indent" > Compute and print on output the edge list of the weighted aggregated graph +associated to the multiplex network given on input. An edge is present in +the aggregated graph if it exists in at least one of the M layers of the +multiplex. +<!--l. 17--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 17--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 17--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 28--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 28--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>the edge list of the aggregated graph +associated to the multiplex network. The edge list is a list of lines in the +format: +<!--l. 28--><p class="indent" >   <span +class="cmti-10x-x-109">ID1 ID2 weight</span> + + + +<!--l. 28--><p class="noindent" >where <span +class="cmti-10x-x-109">ID1 </span>and <span +class="cmti-10x-x-109">ID2 </span>are the IDs of the two nodes and <span +class="cmti-10x-x-109">weight </span>is the number of +layers in which an edge between <span +class="cmti-10x-x-109">ID1 </span>and <span +class="cmti-10x-x-109">ID2 </span>exists. +<!--l. 30--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 30--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 30--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu13.html" >next</a>] [<a +href="mammult_docsu11.html" >prev</a>] [<a +href="mammult_docsu11.html#tailmammult_docsu11.html" >prev-tail</a>] [<a +href="mammult_docsu12.html" >front</a>] [<a +href="mammult_docsu11.html#mammult_docsu12.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu12.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu13.html b/doc/html/mammult_docsu13.html new file mode 100644 index 0000000..02fa0b0 --- /dev/null +++ b/doc/html/mammult_docsu13.html @@ -0,0 +1,94 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.2.0 intersect_layers.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu14.html" >next</a>] [<a +href="mammult_docsu12.html" >prev</a>] [<a +href="mammult_docsu12.html#tailmammult_docsu12.html" >prev-tail</a>] [<a +href="#tailmammult_docsu13.html">tail</a>] [<a +href="mammult_docsu11.html#mammult_docsu13.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x16-150001.1.2"></a><span +class="cmtt-10x-x-109">intersect</span><span +class="cmtt-10x-x-109">_layers.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">intersect</span><span +class="cmbx-10x-x-109">_layers.py </span>- compute the intersection graph associated to a +multiplex. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">intersect</span><span +class="cmbx-10x-x-109">_layers.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer3</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 16--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 16--><p class="indent" > Compute and print on output the edge list of the intersection graph +associated to the multiplex network given on input, where an edge exists only if +it is present on <span +class="cmbx-10x-x-109">all </span>the layers of the multiplex. +<!--l. 16--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 16--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 16--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 26--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 26--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>the edge list of the intersection graph +associated to the multiplex network. The edge list is a list of lines in the +format: +<!--l. 26--><p class="indent" >   <span +class="cmti-10x-x-109">ID1 ID2</span> +<!--l. 26--><p class="noindent" >where <span +class="cmti-10x-x-109">ID1 </span>and <span +class="cmti-10x-x-109">ID2 </span>are the IDs of the two nodes. +<!--l. 28--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 28--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 28--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 153--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu14.html" >next</a>] [<a +href="mammult_docsu12.html" >prev</a>] [<a +href="mammult_docsu12.html#tailmammult_docsu12.html" >prev-tail</a>] [<a +href="mammult_docsu13.html" >front</a>] [<a +href="mammult_docsu11.html#mammult_docsu13.html" >up</a>] </p></div> +<!--l. 153--><p class="indent" > <a + id="tailmammult_docsu13.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu14.html b/doc/html/mammult_docsu14.html new file mode 100644 index 0000000..571c445 --- /dev/null +++ b/doc/html/mammult_docsu14.html @@ -0,0 +1,61 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Node degree, participation coefficient, cartography</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 153--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu15.html" >next</a>] [<a +href="mammult_docsu13.html" >prev</a>] [<a +href="mammult_docsu13.html#tailmammult_docsu13.html" >prev-tail</a>] [<a +href="#tailmammult_docsu14.html">tail</a>] [<a +href="mammult_docse1.html#mammult_docsu14.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">1.1.3 </span> <a + id="x17-160001.1.3"></a>Node degree, participation coefficient, cartography</h4> +<!--l. 155--><p class="noindent" >This section includes programs to compute the total degree and participation +coefficient of each node, and to draw the cartography diagram of a multiplex. +<!--l. 3--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu15.html#x18-170001.1.3"><span +class="cmtt-10x-x-109">overlap</span><span +class="cmtt-10x-x-109">_degree.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu16.html#x19-180001.1.3"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu17.html#x20-190001.1.3"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_deg</span><span +class="cmtt-10x-x-109">_vectors.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu18.html#x21-200001.1.3"><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_columns.py</span></a></span> + </div> + + + + + + + <!--l. 164--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu15.html" >next</a>] [<a +href="mammult_docsu13.html" >prev</a>] [<a +href="mammult_docsu13.html#tailmammult_docsu13.html" >prev-tail</a>] [<a +href="mammult_docsu14.html" >front</a>] [<a +href="mammult_docse1.html#mammult_docsu14.html" >up</a>] </p></div> +<!--l. 164--><p class="indent" > <a + id="tailmammult_docsu14.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu15.html b/doc/html/mammult_docsu15.html new file mode 100644 index 0000000..e1d4712 --- /dev/null +++ b/doc/html/mammult_docsu15.html @@ -0,0 +1,134 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.3.0 overlap_degree.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu16.html" >next</a>] [<a +href="mammult_docsu14.html" >prev</a>] [<a +href="mammult_docsu14.html#tailmammult_docsu14.html" >prev-tail</a>] [<a +href="#tailmammult_docsu15.html">tail</a>] [<a +href="mammult_docsu14.html#mammult_docsu15.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x18-170001.1.3"></a><span +class="cmtt-10x-x-109">overlap</span><span +class="cmtt-10x-x-109">_degree.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">overlap</span><span +class="cmbx-10x-x-109">_degree.py </span>- compute the total (overlapping) degree of all the nodes +of a multiplex and the corresponding Z-score. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">overlap</span><span +class="cmbx-10x-x-109">_degree.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer3</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 29--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 29--><p class="indent" > Compute and print on output the total degree <span +class="cmmi-10x-x-109">o</span><sub><span +class="cmmi-8">i</span></sub> of each node <span +class="cmmi-10x-x-109">i </span>of a +multiplex, defined as: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc0x.png" alt=" ∑ ∑ [α] +oi = aij + α j + + + +" class="math-display" ></center></td></tr></table> +<!--l. 29--><p class="nopar" > +<!--l. 29--><p class="noindent" >and the corresponding Z-score: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc1x.png" alt=" oi − ⟨o⟩ +z(oi) = ---σ--- + o +" class="math-display" ></center></td></tr></table> +<!--l. 29--><p class="nopar" > +<!--l. 29--><p class="noindent" >where <span +class="cmsy-10x-x-109">⟨</span><span +class="cmmi-10x-x-109">o</span><span +class="cmsy-10x-x-109">⟩ </span>and <span +class="cmmi-10x-x-109">σ</span><sub><span +class="cmmi-8">o</span></sub> are, respectively, the mean and the standard deviation of the +total degree computed over all the active nodes of the multiplex. +<!--l. 29--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 29--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 29--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 43--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 43--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: +<!--l. 43--><p class="indent" >   <span +class="cmti-10x-x-109">ID</span><span +class="cmti-10x-x-109">_n deg</span><span +class="cmti-10x-x-109">_n z</span><span +class="cmti-10x-x-109">_n</span> +<!--l. 43--><p class="indent" > where <span +class="cmti-10x-x-109">ID</span><span +class="cmti-10x-x-109">_n </span>is the ID of the node, <span +class="cmti-10x-x-109">deg</span><span +class="cmti-10x-x-109">_n </span>is its total degree, and <span +class="cmti-10x-x-109">z</span><span +class="cmti-10x-x-109">_n </span>is the +corresponding Z-score. +<!--l. 43--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if +a node ID is not present in any of the layer files given as input, the program +considers it as being isolated on all the layers, and the node is omitted from the +output. +<!--l. 45--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 45--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">89</span>, 032804 (2014). +<!--l. 45--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a> + + + + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu16.html" >next</a>] [<a +href="mammult_docsu14.html" >prev</a>] [<a +href="mammult_docsu14.html#tailmammult_docsu14.html" >prev-tail</a>] [<a +href="mammult_docsu15.html" >front</a>] [<a +href="mammult_docsu14.html#mammult_docsu15.html" >up</a>] </p></div> +<!--l. 4--><p class="indent" > <a + id="tailmammult_docsu15.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu16.html b/doc/html/mammult_docsu16.html new file mode 100644 index 0000000..38df999 --- /dev/null +++ b/doc/html/mammult_docsu16.html @@ -0,0 +1,144 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.3.0 cartography_from_layers.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu17.html" >next</a>] [<a +href="mammult_docsu15.html" >prev</a>] [<a +href="mammult_docsu15.html#tailmammult_docsu15.html" >prev-tail</a>] [<a +href="#tailmammult_docsu16.html">tail</a>] [<a +href="mammult_docsu14.html#mammult_docsu16.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x19-180001.1.3"></a><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_layers.py</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">cartography</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_layers.py </span>- compute the total degree and the multiplex +participation coefficient of all the nodes of a multiplex. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">cartography</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_layers.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer3</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 24--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 24--><p class="indent" > Compute and print on output the total degree and the multiplex +participation coefficient <span +class="cmmi-10x-x-109">P</span><sub><span +class="cmmi-8">i</span></sub> for each node <span +class="cmmi-10x-x-109">i </span>of a multiplex. The participation +coefficient is defined as: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc2x.png" alt=" [ M [α] ] + -M---- ∑ ki--2 +Pi = M − 1 1 − ( oi ) + α=1 +" class="math-display" ></center></td></tr></table> +<!--l. 24--><p class="nopar" > +<!--l. 24--><p class="noindent" >Note that <span +class="cmmi-10x-x-109">P</span><sub><span +class="cmmi-8">i</span></sub> takes values in [0<span +class="cmmi-10x-x-109">,</span>1], where <span +class="cmmi-10x-x-109">P</span><sub><span +class="cmmi-8">i</span></sub> = 0 if and only if node <span +class="cmmi-10x-x-109">i </span>is active on +exactly one of the layers, while <span +class="cmmi-10x-x-109">P</span><sub><span +class="cmmi-8">i</span></sub> = 1 if node <span +class="cmmi-10x-x-109">i </span>has equal degree on all the <span +class="cmmi-10x-x-109">M</span> +layers. +<!--l. 24--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 24--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 24--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 43--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 43--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: + + + +<!--l. 43--><p class="indent" >   <span +class="cmti-10x-x-109">deg</span><span +class="cmti-10x-x-109">_n P</span><span +class="cmti-10x-x-109">_n col</span><span +class="cmti-10x-x-109">_n</span> +<!--l. 43--><p class="indent" > where <span +class="cmti-10x-x-109">deg</span><span +class="cmti-10x-x-109">_n </span>is the total degree of node <span +class="cmmi-10x-x-109">n</span>, <span +class="cmti-10x-x-109">P</span><span +class="cmti-10x-x-109">_n </span>is the participation coefficient +of node <span +class="cmmi-10x-x-109">n </span>and <span +class="cmti-10x-x-109">col </span>is the integer representation of the activity bitstring of node <span +class="cmmi-10x-x-109">n</span>, +which is a number between 0 and 2<sup><span +class="cmmi-8">M</span></sup> <span +class="cmsy-10x-x-109">− </span>1. The field <span +class="cmti-10x-x-109">col </span>might be useful for the +visualisation of the multiplex cartography diagram, where it would be +possible to associate different colors to nodes having different node activity +patterns. +<!--l. 43--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., +if a node ID is not present in any of the layer files given as input, the +program considers it as being isolated on all the layers, and is set to +zero. +<!--l. 45--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 45--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">89</span>, 032804 (2014). +<!--l. 45--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu17.html" >next</a>] [<a +href="mammult_docsu15.html" >prev</a>] [<a +href="mammult_docsu15.html#tailmammult_docsu15.html" >prev-tail</a>] [<a +href="mammult_docsu16.html" >front</a>] [<a +href="mammult_docsu14.html#mammult_docsu16.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu16.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu17.html b/doc/html/mammult_docsu17.html new file mode 100644 index 0000000..a118869 --- /dev/null +++ b/doc/html/mammult_docsu17.html @@ -0,0 +1,106 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.3.0 cartography_from_deg_vectors.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu18.html" >next</a>] [<a +href="mammult_docsu16.html" >prev</a>] [<a +href="mammult_docsu16.html#tailmammult_docsu16.html" >prev-tail</a>] [<a +href="#tailmammult_docsu17.html">tail</a>] [<a +href="mammult_docsu14.html#mammult_docsu17.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x20-190001.1.3"></a><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_deg</span><span +class="cmtt-10x-x-109">_vectors.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">cartography</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_deg</span><span +class="cmbx-10x-x-109">_vectors.py </span>- create a multiplex cartography +diagram. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">cartography</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_deg</span><span +class="cmbx-10x-x-109">_vectors.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">node</span><span +class="cmitt-10x-x-109">_deg</span><span +class="cmitt-10x-x-109">_vectors</span><span +class="cmmi-10x-x-109">></span> +<!--l. 14--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 14--><p class="indent" > Compute and print on output the total degree and the multiplex +participation coefficient of all the nodes of a multiplex network whose +list of node degree vectors is provided as input. The input file is in the +format: +<!--l. 14--><p class="indent" >   <span +class="cmti-10x-x-109">IDn</span><span +class="cmti-10x-x-109">_deg1 IDn</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_2 ... IDn</span><span +class="cmti-10x-x-109">_degM</span> +<!--l. 14--><p class="noindent" >where <span +class="cmti-10x-x-109">IDn</span><span +class="cmti-10x-x-109">_degX </span>is the degree of node <span +class="cmmi-10x-x-109">n </span>at layer <span +class="cmmi-10x-x-109">X</span>. The input file can be +generated using the script <span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_degree</span><span +class="cmtt-10x-x-109">_vectors.py</span>. +<!--l. 30--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 30--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: +<!--l. 30--><p class="indent" >   <span +class="cmti-10x-x-109">tot</span><span +class="cmti-10x-x-109">_deg part</span><span +class="cmti-10x-x-109">_coeff</span> +<!--l. 30--><p class="noindent" >where <span +class="cmti-10x-x-109">tot</span><span +class="cmti-10x-x-109">_deg </span>is the total degree of the node and <span +class="cmti-10x-x-109">part</span><span +class="cmti-10x-x-109">_coeff </span>is the corresponding +participation coefficient. +<!--l. 30--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, +so if one of the lines in the input files contains just zeros, the program +considers the corresponding node as being isolated on all the layers, and both +its total degree and multiplex participation coefficient are set equal to +zero. +<!--l. 32--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 32--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">89</span>, 032804 (2014). +<!--l. 32--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a> + + + + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu18.html" >next</a>] [<a +href="mammult_docsu16.html" >prev</a>] [<a +href="mammult_docsu16.html#tailmammult_docsu16.html" >prev-tail</a>] [<a +href="mammult_docsu17.html" >front</a>] [<a +href="mammult_docsu14.html#mammult_docsu17.html" >up</a>] </p></div> +<!--l. 4--><p class="indent" > <a + id="tailmammult_docsu17.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu18.html b/doc/html/mammult_docsu18.html new file mode 100644 index 0000000..ef0ae02 --- /dev/null +++ b/doc/html/mammult_docsu18.html @@ -0,0 +1,102 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.3.0 cartography_from_columns.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu19.html" >next</a>] [<a +href="mammult_docsu17.html" >prev</a>] [<a +href="mammult_docsu17.html#tailmammult_docsu17.html" >prev-tail</a>] [<a +href="#tailmammult_docsu18.html">tail</a>] [<a +href="mammult_docsu14.html#mammult_docsu18.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x21-200001.1.3"></a><span +class="cmtt-10x-x-109">cartography</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_columns.py</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">cartography</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_columns.py </span>- compute total and participation +coefficient of generic structural descriptors of the nodes of a multiplex. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">cartography</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_columns.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">filein</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">col1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">col2</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">col3</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 22--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 22--><p class="indent" > Compute and print on output the sum and the corresponding participation +coefficient of a generic structural descriptor of the nodes of a multiplex. +<!--l. 22--><p class="noindent" >The input file is a generic collection of single-space-separated columns, where +each line corresponds to a node. The user must specify the IDs of the columns +which contain the node structural descriptors to be used in the cartography +diagram. Columns IDs start from ZERO. For example: +<!--l. 22--><p class="indent" > <span +class="cmbx-10x-x-109">python cartography</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_layers.py filein.txt 0 2 4 6 8</span> +<!--l. 22--><p class="noindent" >will create a cartography diagram assuming that the multiplex network has five +layers, and that the node structural descriptors at each layers are contained in +the first (0), third (2), fifth (4), seventh (6) and nineth (8) columns of each +row. +<!--l. 33--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 33--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: +<!--l. 33--><p class="indent" >   <span +class="cmti-10x-x-109">tot</span><span +class="cmti-10x-x-109">_n P</span><span +class="cmti-10x-x-109">_n</span> +<!--l. 33--><p class="indent" > where <span +class="cmti-10x-x-109">tot</span><span +class="cmti-10x-x-109">_n </span>is the sum over the layers of the considered structural descriptor +for node <span +class="cmmi-10x-x-109">n</span>, and <span +class="cmti-10x-x-109">P</span><span +class="cmti-10x-x-109">_n </span>is the associated participation coefficient +<!--l. 35--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 35--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 35--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 164--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu19.html" >next</a>] [<a +href="mammult_docsu17.html" >prev</a>] [<a +href="mammult_docsu17.html#tailmammult_docsu17.html" >prev-tail</a>] [<a +href="mammult_docsu18.html" >front</a>] [<a +href="mammult_docsu14.html#mammult_docsu18.html" >up</a>] </p></div> +<!--l. 164--><p class="indent" > <a + id="tailmammult_docsu18.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu19.html b/doc/html/mammult_docsu19.html new file mode 100644 index 0000000..9f13aa6 --- /dev/null +++ b/doc/html/mammult_docsu19.html @@ -0,0 +1,52 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Edge overlap, reinforcement</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 164--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu20.html" >next</a>] [<a +href="mammult_docsu18.html" >prev</a>] [<a +href="mammult_docsu18.html#tailmammult_docsu18.html" >prev-tail</a>] [<a +href="#tailmammult_docsu19.html">tail</a>] [<a +href="mammult_docse1.html#mammult_docsu19.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">1.1.4 </span> <a + id="x22-210001.1.4"></a>Edge overlap, reinforcement</h4> +<!--l. 165--><p class="noindent" >This section includes programs to compute the egde overlap and to evaulate the +edge reinforcement effect. +<!--l. 4--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu20.html#x23-220001.1.4"><span +class="cmtt-10x-x-109">edge</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu21.html#x24-230001.1.4"><span +class="cmtt-10x-x-109">avg</span><span +class="cmtt-10x-x-109">_edge</span><span +class="cmtt-10x-x-109">_overlap.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu22.html#x25-240001.1.4"><span +class="cmtt-10x-x-109">reinforcement.py</span></a></span> + </div> + + + + + + <!--l. 172--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu20.html" >next</a>] [<a +href="mammult_docsu18.html" >prev</a>] [<a +href="mammult_docsu18.html#tailmammult_docsu18.html" >prev-tail</a>] [<a +href="mammult_docsu19.html" >front</a>] [<a +href="mammult_docse1.html#mammult_docsu19.html" >up</a>] </p></div> +<!--l. 172--><p class="indent" > <a + id="tailmammult_docsu19.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu2.html b/doc/html/mammult_docsu2.html new file mode 100644 index 0000000..2b19954 --- /dev/null +++ b/doc/html/mammult_docsu2.html @@ -0,0 +1,86 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 node_activity.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu3.html" >next</a>] [<a +href="mammult_docsu1.html" >prev</a>] [<a +href="mammult_docsu1.html#tailmammult_docsu1.html" >prev-tail</a>] [<a +href="#tailmammult_docsu2.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu2.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x5-40001.1.1"></a><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_activity.py</span></h5> +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">node</span><span +class="cmbx-10x-x-109">_activity.py </span>- compute the activity of the nodes of a multiplex, i.e. the +number of layers where each node is not isolated. +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">node</span><span +class="cmbx-10x-x-109">_activity.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 19--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 19--><p class="indent" > Compute and print on output the activity of the nodes of a multiplex +network, whose layers are given as input in the files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, etc. +<!--l. 19--><p class="indent" > Each file contains the (undirected) edge list of a layer, and each line is in the +format: +<!--l. 19--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 19--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 22--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 22--><p class="indent" > A list of lines, where the n-th line is the value of activity of the n-th node, +starting from <span +class="cmbx-10x-x-109">0</span>. +<!--l. 24--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 24--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 24--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 8--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu3.html" >next</a>] [<a +href="mammult_docsu1.html" >prev</a>] [<a +href="mammult_docsu1.html#tailmammult_docsu1.html" >prev-tail</a>] [<a +href="mammult_docsu2.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu2.html" >up</a>] </p></div> +<!--l. 8--><p class="indent" > <a + id="tailmammult_docsu2.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu20.html b/doc/html/mammult_docsu20.html new file mode 100644 index 0000000..02f16da --- /dev/null +++ b/doc/html/mammult_docsu20.html @@ -0,0 +1,115 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.4.0 edge_overlap.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu21.html" >next</a>] [<a +href="mammult_docsu19.html" >prev</a>] [<a +href="mammult_docsu19.html#tailmammult_docsu19.html" >prev-tail</a>] [<a +href="#tailmammult_docsu20.html">tail</a>] [<a +href="mammult_docsu19.html#mammult_docsu20.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x23-220001.1.4"></a><span +class="cmtt-10x-x-109">edge</span><span +class="cmtt-10x-x-109">_overlap.py</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">edge</span><span +class="cmbx-10x-x-109">_overlap.py </span>- compute the edge overlap of all the edges of the +multiplex. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">edge</span><span +class="cmbx-10x-x-109">_overlap.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 25--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 25--><p class="indent" > Compute and print on output the edge overlap <span +class="cmmi-10x-x-109">o</span><sub><span +class="cmmi-8">ij</span></sub> of each edge of the +multiplex. Given a pair of nodes (<span +class="cmmi-10x-x-109">i,j</span>) that are directly connected on at least one +of the <span +class="cmmi-10x-x-109">M </span>layers, the edge overlap <span +class="cmmi-10x-x-109">o</span><sub><span +class="cmmi-8">ij</span></sub> is defined as: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc3x.png" alt=" ∑ [α] +oij = aij + α + + + +" class="math-display" ></center></td></tr></table> +<!--l. 25--><p class="nopar" > +<!--l. 25--><p class="noindent" >i.e., the number of layers on which the edge (<span +class="cmmi-10x-x-109">i,j</span>) exists. +<!--l. 25--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 25--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 25--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 34--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 34--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: +<!--l. 34--><p class="indent" >   <span +class="cmti-10x-x-109">ID</span><span +class="cmti-10x-x-109">_1 ID</span><span +class="cmti-10x-x-109">_2 overlap</span> +<!--l. 34--><p class="noindent" >where <span +class="cmti-10x-x-109">ID</span><span +class="cmti-10x-x-109">_1 </span>and <span +class="cmti-10x-x-109">ID</span><span +class="cmti-10x-x-109">_2 </span>are the IDs of the end-points of the edge, and <span +class="cmti-10x-x-109">overlap </span>is +the number of layers in which the edge exists. +<!--l. 36--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 36--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">89</span>, 032804 (2014). +<!--l. 36--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu21.html" >next</a>] [<a +href="mammult_docsu19.html" >prev</a>] [<a +href="mammult_docsu19.html#tailmammult_docsu19.html" >prev-tail</a>] [<a +href="mammult_docsu20.html" >front</a>] [<a +href="mammult_docsu19.html#mammult_docsu20.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu20.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu21.html b/doc/html/mammult_docsu21.html new file mode 100644 index 0000000..87045b2 --- /dev/null +++ b/doc/html/mammult_docsu21.html @@ -0,0 +1,125 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.4.0 avg_edge_overlap.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu22.html" >next</a>] [<a +href="mammult_docsu20.html" >prev</a>] [<a +href="mammult_docsu20.html#tailmammult_docsu20.html" >prev-tail</a>] [<a +href="#tailmammult_docsu21.html">tail</a>] [<a +href="mammult_docsu19.html#mammult_docsu21.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x24-230001.1.4"></a><span +class="cmtt-10x-x-109">avg</span><span +class="cmtt-10x-x-109">_edge</span><span +class="cmtt-10x-x-109">_overlap.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">avg</span><span +class="cmbx-10x-x-109">_edge</span><span +class="cmbx-10x-x-109">_overlap.py </span>- compute the average edge overlap of a multiplex. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">avg</span><span +class="cmbx-10x-x-109">_edge</span><span +class="cmbx-10x-x-109">_overlap.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 29--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 29--><p class="indent" > Compute and print on output the average edge overlap + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc4x.png" alt=" ∑ ∑ ∑ [α] + ∗ ∑--∑-i--j>i---αaij---- +ω = i j>i(1− δ ∑ [α]) + 0, α aij +" class="math-display" ></center></td></tr></table> +<!--l. 29--><p class="nopar" > +<!--l. 29--><p class="noindent" >i.e., the expected <span +class="cmti-10x-x-109">number </span>of layers on which an edge of the multiplex exists, and +the corresponding normalised quantity: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc5x.png" alt=" ∑ ∑ ∑ a[α] +ω = ---∑--∑i--j>i--α--ij----- + M i j>i(1− δ0,∑α a[iαj] ) +" class="math-display" ></center></td></tr></table> +<!--l. 29--><p class="nopar" > +<!--l. 29--><p class="noindent" >that is the expected <span +class="cmti-10x-x-109">fraction </span>of layers on which an edge of the multiplex is +present. +<!--l. 29--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 29--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 29--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 38--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 38--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a single line, in the format: +<!--l. 38--><p class="indent" >   <span +class="cmti-10x-x-109">omega</span><span +class="cmti-10x-x-109">_star omega</span> +<!--l. 38--><p class="noindent" >where <span +class="cmti-10x-x-109">omega</span><span +class="cmti-10x-x-109">_star </span>and <span +class="cmti-10x-x-109">omega </span>are, respectively, the expected number and fraction +of layers in which an edge is present. +<!--l. 42--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 42--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">89</span>, 032804 (2014). +<!--l. 42--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a> +<!--l. 42--><p class="indent" > L. Lacasa, V. Nicosia, V. Latora, <span +class="cmti-10x-x-109">“Network structure of multivariate time</span> +<span +class="cmti-10x-x-109">series”</span>, accepted for publication in Scientific Reports, arxiv:1408.0925 +(2015). +<!--l. 42--><p class="indent" > Link to paper: <a +href="http://arxiv.org/abs/1408.0925" class="url" ><span +class="cmtt-10x-x-109">http://arxiv.org/abs/1408.0925</span></a> + + + + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu22.html" >next</a>] [<a +href="mammult_docsu20.html" >prev</a>] [<a +href="mammult_docsu20.html#tailmammult_docsu20.html" >prev-tail</a>] [<a +href="mammult_docsu21.html" >front</a>] [<a +href="mammult_docsu19.html#mammult_docsu21.html" >up</a>] </p></div> +<!--l. 7--><p class="indent" > <a + id="tailmammult_docsu21.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu22.html b/doc/html/mammult_docsu22.html new file mode 100644 index 0000000..b28a026 --- /dev/null +++ b/doc/html/mammult_docsu22.html @@ -0,0 +1,92 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.4.0 reinforcement.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse2.html" >next</a>] [<a +href="mammult_docsu21.html" >prev</a>] [<a +href="mammult_docsu21.html#tailmammult_docsu21.html" >prev-tail</a>] [<a +href="#tailmammult_docsu22.html">tail</a>] [<a +href="mammult_docsu19.html#mammult_docsu22.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x25-240001.1.4"></a><span +class="cmtt-10x-x-109">reinforcement.py</span></h5> +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">reinforcement.py </span>- compute the probability to have a link between two +nodes in layer 1 given their weight in layer 2. +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">reinforcement.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> < N</span><sub><span +class="cmmi-8">bins</span></sub> <span +class="cmmi-10x-x-109">> < min</span><sub><span +class="cmmi-8">value</span></sub> <span +class="cmmi-10x-x-109">></span> +<span +class="cmmi-10x-x-109">< max</span><sub><span +class="cmmi-8">value</span></sub> <span +class="cmmi-10x-x-109">></span> +<!--l. 17--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 17--><p class="indent" > Compute and print on output the probability to have a link between two +nodes in layer 1 given their weight in layer 2. As input are given the files <span +class="cmti-10x-x-109">layer1</span>, +<span +class="cmti-10x-x-109">layer2</span>, the number of bins for the link weights of the second layer, the minimum +and the maximum values of the binning. +<!--l. 17--><p class="indent" > The first file contains the binary edge list of layer 1, the second file contains +the weighted edge list of layer 2. each line is in the format: +<!--l. 17--><p class="indent" >   <span +class="cmti-10x-x-109">bin</span><span +class="cmti-10x-x-109">_min bin</span><span +class="cmti-10x-x-109">_max freq</span> +<!--l. 17--><p class="indent" > where <span +class="cmti-10x-x-109">bin</span><span +class="cmti-10x-x-109">_min </span>and <span +class="cmti-10x-x-109">bin</span><span +class="cmti-10x-x-109">_max </span>are the minimum and maximum values of the +link weights of layer 2 in that binning, and <span +class="cmti-10x-x-109">freq </span>is the probability to have a link +on layer 1 given such weight in layer 2. +<!--l. 19--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 19--><p class="indent" > A list of lines, where the n-th line is the minimum and maximum values of +the weight of the links in layer 2 in the n-th bin, and the frequency to have a link +on layer 2 given that weight. +<!--l. 21--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 21--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">89</span>, 032804 (2014). +<!--l. 21--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a> + + + + <!--l. 172--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse2.html" >next</a>] [<a +href="mammult_docsu21.html" >prev</a>] [<a +href="mammult_docsu21.html#tailmammult_docsu21.html" >prev-tail</a>] [<a +href="mammult_docsu22.html" >front</a>] [<a +href="mammult_docsu19.html#mammult_docsu22.html" >up</a>] </p></div> +<!--l. 172--><p class="indent" > <a + id="tailmammult_docsu22.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu23.html b/doc/html/mammult_docsu23.html new file mode 100644 index 0000000..113a718 --- /dev/null +++ b/doc/html/mammult_docsu23.html @@ -0,0 +1,54 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Node ranking</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 174--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu24.html" >next</a>] [<a +href="mammult_docse2.html" >prev</a>] [<a +href="mammult_docse2.html#tailmammult_docse2.html" >prev-tail</a>] [<a +href="#tailmammult_docsu23.html">tail</a>] [<a +href="mammult_docse2.html#mammult_docsu23.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">1.2.1 </span> <a + id="x27-260001.2.1"></a>Node ranking</h4> +<!--l. 176--><p class="noindent" >This section includes various utilities to compute and compare node rankings +induced by any generic structural node property, including degree at different +layers. +<!--l. 3--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu24.html#x28-270001.2.1"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_nodes.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu25.html#x29-280001.2.1"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_nodes</span><span +class="cmtt-10x-x-109">_thresh.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu26.html#x30-290001.2.1"><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_occurrence.py</span></a></span> + </div> + + + + + + <!--l. 184--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu24.html" >next</a>] [<a +href="mammult_docse2.html" >prev</a>] [<a +href="mammult_docse2.html#tailmammult_docse2.html" >prev-tail</a>] [<a +href="mammult_docsu23.html" >front</a>] [<a +href="mammult_docse2.html#mammult_docsu23.html" >up</a>] </p></div> +<!--l. 184--><p class="indent" > <a + id="tailmammult_docsu23.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu24.html b/doc/html/mammult_docsu24.html new file mode 100644 index 0000000..7968150 --- /dev/null +++ b/doc/html/mammult_docsu24.html @@ -0,0 +1,79 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.1.0 rank_nodes.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu25.html" >next</a>] [<a +href="mammult_docsu23.html" >prev</a>] [<a +href="mammult_docsu23.html#tailmammult_docsu23.html" >prev-tail</a>] [<a +href="#tailmammult_docsu24.html">tail</a>] [<a +href="mammult_docsu23.html#mammult_docsu24.html" >up</a>] </p></div> + + + + <h5 class="subsubsectionHead"><a + id="x28-270001.2.1"></a><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_nodes.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">rank</span><span +class="cmbx-10x-x-109">_nodes.py </span>- rank the nodes of a layer according to a given structural +descriptor. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">rank</span><span +class="cmbx-10x-x-109">_nodes.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">prop</span><span +class="cmitt-10x-x-109">_file</span><span +class="cmmi-10x-x-109">></span> +<!--l. 13--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 13--><p class="indent" > Get a file as input, whose n-th line corresponds to the value of a certain +property of the n-th node, and rank the nodes according to that property, taking +into account ranking ties properly. +<!--l. 13--><p class="indent" > For example, if <span +class="cmti-10x-x-109">propfile </span>contains the degrees of the nodes at a certain +layer of the multiplex, the computes the ranking induced by degrees, +where the node with the highest degree will be assigned a rank equal to <span +class="cmbx-10x-x-109">1</span> +(one). +<!--l. 17--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 17--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains the +rank of the n-th node corresponding to the values of the structural descriptor +provided in the input file. +<!--l. 19--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 19--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 19--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu25.html" >next</a>] [<a +href="mammult_docsu23.html" >prev</a>] [<a +href="mammult_docsu23.html#tailmammult_docsu23.html" >prev-tail</a>] [<a +href="mammult_docsu24.html" >front</a>] [<a +href="mammult_docsu23.html#mammult_docsu24.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu24.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu25.html b/doc/html/mammult_docsu25.html new file mode 100644 index 0000000..43094cd --- /dev/null +++ b/doc/html/mammult_docsu25.html @@ -0,0 +1,81 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.1.0 rank_nodes_thresh.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu26.html" >next</a>] [<a +href="mammult_docsu24.html" >prev</a>] [<a +href="mammult_docsu24.html#tailmammult_docsu24.html" >prev-tail</a>] [<a +href="#tailmammult_docsu25.html">tail</a>] [<a +href="mammult_docsu23.html#mammult_docsu25.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x29-280001.2.1"></a><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_nodes</span><span +class="cmtt-10x-x-109">_thresh.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">rank</span><span +class="cmbx-10x-x-109">_nodes</span><span +class="cmbx-10x-x-109">_thresh.py </span>- rank the nodes of a layer whose value of a given +structural descriptor is above a threshold. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">rank</span><span +class="cmbx-10x-x-109">_nodes</span><span +class="cmbx-10x-x-109">_thresh.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">prop</span><span +class="cmitt-10x-x-109">_file</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">thresh</span><span +class="cmmi-10x-x-109">></span> +<!--l. 10--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 10--><p class="indent" > Get a file as input, whose n-th line corresponds to the value of a certain +property of the n-th node, and rank the nodes according to that property, taking +into account ranking ties properly. The rank of all the nodes whose value of the +structural descriptor is smaller than the threshold <span +class="cmti-10x-x-109">thresh </span>specified as second +parameter is set to <span +class="cmbx-10x-x-109">0 </span>(ZERO). +<!--l. 16--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 16--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains the +rank of the n-th node corresponding to the values of the structural descriptor +provided in the input file, or zero if such desxriptor is below the specified +threshold <span +class="cmti-10x-x-109">thresh</span>. +<!--l. 18--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 18--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 18--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu26.html" >next</a>] [<a +href="mammult_docsu24.html" >prev</a>] [<a +href="mammult_docsu24.html#tailmammult_docsu24.html" >prev-tail</a>] [<a +href="mammult_docsu25.html" >front</a>] [<a +href="mammult_docsu23.html#mammult_docsu25.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu25.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu26.html b/doc/html/mammult_docsu26.html new file mode 100644 index 0000000..c13e9a2 --- /dev/null +++ b/doc/html/mammult_docsu26.html @@ -0,0 +1,87 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.1.0 rank_occurrence.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu27.html" >next</a>] [<a +href="mammult_docsu25.html" >prev</a>] [<a +href="mammult_docsu25.html#tailmammult_docsu25.html" >prev-tail</a>] [<a +href="#tailmammult_docsu26.html">tail</a>] [<a +href="mammult_docsu23.html#mammult_docsu26.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x30-290001.2.1"></a><span +class="cmtt-10x-x-109">rank</span><span +class="cmtt-10x-x-109">_occurrence.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">rank</span><span +class="cmbx-10x-x-109">_occurrence.py </span>- compute the intersection of two rankings. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">rank</span><span +class="cmbx-10x-x-109">_occurrence.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">rank1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">rank2</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">increment</span><span +class="cmmi-10x-x-109">></span> +<!--l. 14--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 14--><p class="indent" > Get two rankings <span +class="cmti-10x-x-109">rank1 </span>and <span +class="cmti-10x-x-109">rank2 </span>and compute the size of the <span +class="cmti-10x-x-109">k</span>-intersection, +i.e. the number of elements which are present in the first k positions of both +rankings, as a function of <span +class="cmti-10x-x-109">k</span>. The parameter <span +class="cmti-10x-x-109">increment </span>determines the distance +between two subsequent values of <span +class="cmti-10x-x-109">k</span>. +<!--l. 14--><p class="indent" > Each input file is a list of node IDs, one per line, where the first line contains +the ID of the highest ranked node. +<!--l. 22--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 22--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: +<!--l. 22--><p class="indent" >   <span +class="cmti-10x-x-109">k num</span><span +class="cmti-10x-x-109">_k</span> +<!--l. 22--><p class="indent" > where <span +class="cmti-10x-x-109">num</span><span +class="cmti-10x-x-109">_k </span>is the number of nodes which are present in the first <span +class="cmti-10x-x-109">k </span>positions +of both rankings. +<!--l. 24--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 24--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 24--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 184--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu27.html" >next</a>] [<a +href="mammult_docsu25.html" >prev</a>] [<a +href="mammult_docsu25.html#tailmammult_docsu25.html" >prev-tail</a>] [<a +href="mammult_docsu26.html" >front</a>] [<a +href="mammult_docsu23.html#mammult_docsu26.html" >up</a>] </p></div> +<!--l. 184--><p class="indent" > <a + id="tailmammult_docsu26.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu27.html b/doc/html/mammult_docsu27.html new file mode 100644 index 0000000..2a20dd4 --- /dev/null +++ b/doc/html/mammult_docsu27.html @@ -0,0 +1,52 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Interlayer degree correlation coefficients</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 184--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu28.html" >next</a>] [<a +href="mammult_docsu26.html" >prev</a>] [<a +href="mammult_docsu26.html#tailmammult_docsu26.html" >prev-tail</a>] [<a +href="#tailmammult_docsu27.html">tail</a>] [<a +href="mammult_docse2.html#mammult_docsu27.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">1.2.2 </span> <a + id="x31-300001.2.2"></a>Interlayer degree correlation coefficients</h4> +<!--l. 186--><p class="noindent" >This section includes programs for the computation of various inter-layer degree +correlation coefficients. +<!--l. 4--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu28.html#x32-310001.2.2"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_pearson.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu29.html#x33-320001.2.2"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_rho.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu30.html#x34-330001.2.2"><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_tau.py</span></a></span> + </div> + + + + + + <!--l. 194--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu28.html" >next</a>] [<a +href="mammult_docsu26.html" >prev</a>] [<a +href="mammult_docsu26.html#tailmammult_docsu26.html" >prev-tail</a>] [<a +href="mammult_docsu27.html" >front</a>] [<a +href="mammult_docse2.html#mammult_docsu27.html" >up</a>] </p></div> +<!--l. 194--><p class="indent" > <a + id="tailmammult_docsu27.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu28.html b/doc/html/mammult_docsu28.html new file mode 100644 index 0000000..05c2082 --- /dev/null +++ b/doc/html/mammult_docsu28.html @@ -0,0 +1,96 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.2.0 compute_pearson.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu29.html" >next</a>] [<a +href="mammult_docsu27.html" >prev</a>] [<a +href="mammult_docsu27.html#tailmammult_docsu27.html" >prev-tail</a>] [<a +href="#tailmammult_docsu28.html">tail</a>] [<a +href="mammult_docsu27.html#mammult_docsu28.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x32-310001.2.2"></a><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_pearson.py</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">compute</span><span +class="cmbx-10x-x-109">_pearson.py </span>- compute the Pearson’s linear correlation coefficient +between two node properties. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">compute</span><span +class="cmbx-10x-x-109">_pearson.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">file1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">file2</span><span +class="cmmi-10x-x-109">></span> +<!--l. 16--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 16--><p class="indent" > Compute the Pearson’s linear correlation coefficient between two sets of +(either integer- or real-valued) node properties provided in the input files +<span +class="cmti-10x-x-109">file1 </span>and <span +class="cmti-10x-x-109">file2</span>. Each input file contains a list of lines, where the n-th line +contains the value of a node property for the n-th node. For instance, <span +class="cmti-10x-x-109">file1</span> +and <span +class="cmti-10x-x-109">file2 </span>might contain the degrees of nodes at two distinct layers of a +multiplex. However, the program is pretty general and can be used to +compute the Pearson’s correlation coeffcient between any pairs of node +properties. +<!--l. 21--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 21--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>the value of the Pearson’s linear correlation +coefficient between the two sets of node properties. +<!--l. 28--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> + + + +<!--l. 28--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 28--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> +<!--l. 28--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 28--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<!--l. 28--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">90</span>, 042807 (2014). +<!--l. 28--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu29.html" >next</a>] [<a +href="mammult_docsu27.html" >prev</a>] [<a +href="mammult_docsu27.html#tailmammult_docsu27.html" >prev-tail</a>] [<a +href="mammult_docsu28.html" >front</a>] [<a +href="mammult_docsu27.html#mammult_docsu28.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu28.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu29.html b/doc/html/mammult_docsu29.html new file mode 100644 index 0000000..973c83d --- /dev/null +++ b/doc/html/mammult_docsu29.html @@ -0,0 +1,100 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.2.0 compute_rho.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu30.html" >next</a>] [<a +href="mammult_docsu28.html" >prev</a>] [<a +href="mammult_docsu28.html#tailmammult_docsu28.html" >prev-tail</a>] [<a +href="#tailmammult_docsu29.html">tail</a>] [<a +href="mammult_docsu27.html#mammult_docsu29.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x33-320001.2.2"></a><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_rho.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">compute</span><span +class="cmbx-10x-x-109">_rho.py </span>- compute the Spearman’s rank correlation coefficient <span +class="cmmi-10x-x-109">ρ</span> +between two rankings. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">compute</span><span +class="cmbx-10x-x-109">_rho.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">file1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">file2</span><span +class="cmmi-10x-x-109">></span> +<!--l. 20--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 20--><p class="indent" > Compute the Spearman’s rank correlation coefficient <span +class="cmmi-10x-x-109">ρ </span>between two rankings +provided in the input files <span +class="cmti-10x-x-109">file1 </span>and <span +class="cmti-10x-x-109">file2</span>. Each input file contains a list of lines, +where the n-th line contains the value of rank of the n-th node. For instance, <span +class="cmti-10x-x-109">file1</span> +and <span +class="cmti-10x-x-109">file2 </span>might contain the ranks of nodes induced by the degree sequences of +two distinct layers of a multiplex. +<!--l. 20--><p class="indent" > However, the program is pretty general and can be used to compute +the Spearman’s rank correlation coefficient between any generic pair of +rankings. +<!--l. 20--><p class="indent" > N.B.: A C implementation of this program, with the same interface is also +available in the executable file <span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_rho</span>. +<!--l. 25--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 25--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>the value of the Spearman’s rank correlation +coefficient <span +class="cmmi-10x-x-109">ρ </span>between the two rankings provided as input. +<!--l. 32--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 32--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 32--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> +<!--l. 32--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 32--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<!--l. 32--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">90</span>, 042807 (2014). +<!--l. 32--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu30.html" >next</a>] [<a +href="mammult_docsu28.html" >prev</a>] [<a +href="mammult_docsu28.html#tailmammult_docsu28.html" >prev-tail</a>] [<a +href="mammult_docsu29.html" >front</a>] [<a +href="mammult_docsu27.html#mammult_docsu29.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu29.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu3.html b/doc/html/mammult_docsu3.html new file mode 100644 index 0000000..cd582bb --- /dev/null +++ b/doc/html/mammult_docsu3.html @@ -0,0 +1,87 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 layer_activity.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 8--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu4.html" >next</a>] [<a +href="mammult_docsu2.html" >prev</a>] [<a +href="mammult_docsu2.html#tailmammult_docsu2.html" >prev-tail</a>] [<a +href="#tailmammult_docsu3.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu3.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x6-50001.1.1"></a><span +class="cmtt-10x-x-109">layer</span><span +class="cmtt-10x-x-109">_activity.py</span></h5> +<!--l. 8--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 8--><p class="indent" > <span +class="cmbx-10x-x-109">layer</span><span +class="cmbx-10x-x-109">_activity.py </span>- compute the activity of the layers of a multiplex, i.e. the +number of active nodes on each layer. +<!--l. 8--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 8--><p class="indent" > <span +class="cmbx-10x-x-109">layer</span><span +class="cmbx-10x-x-109">_activity.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 20--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 20--><p class="indent" > Compute and print on output the activity of the layers of a multiplex +network, where the layers are given as input in the files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, +etc. +<!--l. 20--><p class="indent" > Each file contains the (undirected) edge list of a layer, and each line is in the +format: +<!--l. 20--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 20--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 23--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 23--><p class="indent" > A listof lines, where the n-th line is the value of activity of the n-th layer, +starting from <span +class="cmbx-10x-x-109">0</span>. +<!--l. 25--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 25--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 25--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu4.html" >next</a>] [<a +href="mammult_docsu2.html" >prev</a>] [<a +href="mammult_docsu2.html#tailmammult_docsu2.html" >prev-tail</a>] [<a +href="mammult_docsu3.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu3.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu3.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu30.html b/doc/html/mammult_docsu30.html new file mode 100644 index 0000000..c743f7b --- /dev/null +++ b/doc/html/mammult_docsu30.html @@ -0,0 +1,100 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.2.0 compute_tau.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu31.html" >next</a>] [<a +href="mammult_docsu29.html" >prev</a>] [<a +href="mammult_docsu29.html#tailmammult_docsu29.html" >prev-tail</a>] [<a +href="#tailmammult_docsu30.html">tail</a>] [<a +href="mammult_docsu27.html#mammult_docsu30.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x34-330001.2.2"></a><span +class="cmtt-10x-x-109">compute</span><span +class="cmtt-10x-x-109">_tau.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">compute</span><span +class="cmbx-10x-x-109">_tau.py </span>- compute the Kendall’s rank correlation coefficient <span +class="cmmi-10x-x-109">τ</span><sub><span +class="cmmi-8">b</span></sub> +between two rankings. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">compute</span><span +class="cmbx-10x-x-109">_tau.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">file1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">file2</span><span +class="cmmi-10x-x-109">></span> +<!--l. 19--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 19--><p class="indent" > Compute the Kendall’s rank correlation coefficient <span +class="cmmi-10x-x-109">τ</span><sub><span +class="cmmi-8">b</span></sub> between two rankings +provided in the input files <span +class="cmti-10x-x-109">file1 </span>and <span +class="cmti-10x-x-109">file2</span>. Each input file contains a list of lines, +where the n-th line contains the value of rank of the n-th node. For instance, <span +class="cmti-10x-x-109">file1</span> +and <span +class="cmti-10x-x-109">file2 </span>might contain the ranks of nodes induced by the degree sequences of +two distinct layers of a multiplex. +<!--l. 19--><p class="indent" > However, the program is pretty general and can be used to compute +the Kendall’s rank correlation coefficient between any generic pair of +rankings. +<!--l. 19--><p class="indent" > N.B.: This implementation takes properly into account rank ties. +<!--l. 24--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 24--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>the value of the Kendall’s rank correlation +coefficient <span +class="cmmi-10x-x-109">τ</span><sub><span +class="cmmi-8">b</span></sub> between the two rankings provided as input. +<!--l. 31--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 31--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 31--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> +<!--l. 31--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 31--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<!--l. 31--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">90</span>, 042807 (2014). +<!--l. 31--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a> + + + + <!--l. 194--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu31.html" >next</a>] [<a +href="mammult_docsu29.html" >prev</a>] [<a +href="mammult_docsu29.html#tailmammult_docsu29.html" >prev-tail</a>] [<a +href="mammult_docsu30.html" >front</a>] [<a +href="mammult_docsu27.html#mammult_docsu30.html" >up</a>] </p></div> +<!--l. 194--><p class="indent" > <a + id="tailmammult_docsu30.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu31.html b/doc/html/mammult_docsu31.html new file mode 100644 index 0000000..50ae7f8 --- /dev/null +++ b/doc/html/mammult_docsu31.html @@ -0,0 +1,62 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Interlayer degree correlation functions</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 194--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu32.html" >next</a>] [<a +href="mammult_docsu30.html" >prev</a>] [<a +href="mammult_docsu30.html#tailmammult_docsu30.html" >prev-tail</a>] [<a +href="#tailmammult_docsu31.html">tail</a>] [<a +href="mammult_docse2.html#mammult_docsu31.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">1.2.3 </span> <a + id="x35-340001.2.3"></a>Interlayer degree correlation functions</h4> +<!--l. 196--><p class="noindent" >This section includes programs to compute intra-layer and inter-layer degree +correlation functions, and to fit those functions with a power-law. +<!--l. 1--><p class="indent" > M + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu32.html#x36-350001.2.3"><span +class="cmtt-10x-x-109">dump</span><span +class="cmtt-10x-x-109">_k</span><span +class="cmtt-10x-x-109">_q</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu33.html#x37-360001.2.3"><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_layers.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu34.html#x38-370001.2.3"><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_degrees.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu35.html#x39-380001.2.3"><span +class="cmtt-10x-x-109">fit</span><span +class="cmtt-10x-x-109">_knn</span></a></span> + </div> + + + + + + + <!--l. 208--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu32.html" >next</a>] [<a +href="mammult_docsu30.html" >prev</a>] [<a +href="mammult_docsu30.html#tailmammult_docsu30.html" >prev-tail</a>] [<a +href="mammult_docsu31.html" >front</a>] [<a +href="mammult_docse2.html#mammult_docsu31.html" >up</a>] </p></div> +<!--l. 208--><p class="indent" > <a + id="tailmammult_docsu31.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu32.html b/doc/html/mammult_docsu32.html new file mode 100644 index 0000000..bfda1c1 --- /dev/null +++ b/doc/html/mammult_docsu32.html @@ -0,0 +1,123 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.3.0 dump_k_q</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu33.html" >next</a>] [<a +href="mammult_docsu31.html" >prev</a>] [<a +href="mammult_docsu31.html#tailmammult_docsu31.html" >prev-tail</a>] [<a +href="#tailmammult_docsu32.html">tail</a>] [<a +href="mammult_docsu31.html#mammult_docsu32.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x36-350001.2.3"></a><span +class="cmtt-10x-x-109">dump</span><span +class="cmtt-10x-x-109">_k</span><span +class="cmtt-10x-x-109">_q</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">dump</span><span +class="cmbx-10x-x-109">_k</span><span +class="cmbx-10x-x-109">_q </span>- compute the degree sequences of two layers of a multiplex. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">dump</span><span +class="cmbx-10x-x-109">_k</span><span +class="cmbx-10x-x-109">_q </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">pairing</span><span +class="cmmi-10x-x-109">></span> +<!--l. 26--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 26--><p class="indent" > Compute and dump on <span +class="cmtt-10x-x-109">stdout </span>the degree sequences of two layers of a +multiplex. The input files <span +class="cmti-10x-x-109">layer1 </span>and <span +class="cmti-10x-x-109">layer2 </span>contain the (undirected) edge lists of +the two layers, and each line is in the format: +<!--l. 26--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 26--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 26--><p class="indent" > The third file <span +class="cmti-10x-x-109">pairing </span>is a list of lines in the format: +<!--l. 26--><p class="indent" >   <span +class="cmti-10x-x-109">IDL1 IDL2</span> +<!--l. 26--><p class="indent" > where <span +class="cmti-10x-x-109">IDL1 </span>is the ID of a node on layer 1 and <span +class="cmti-10x-x-109">IDL2 </span>is the ID of the same +node on layer 2. For instance, the line: +<!--l. 26--><p class="indent" >   <span +class="cmti-10x-x-109">5 27</span> +<!--l. 26--><p class="indent" > indicates that node 5 on layer 1 has ID 27 on layer 2. +<!--l. 35--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> + + + +<!--l. 35--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>the degree of each node on the two layers, in +the format: +<!--l. 35--><p class="indent" >   <span +class="cmti-10x-x-109">ki qi</span> +<!--l. 35--><p class="indent" > where <span +class="cmti-10x-x-109">ki </span>is the degree of node <span +class="cmti-10x-x-109">i </span>on layer 1 and <span +class="cmti-10x-x-109">qi </span>is the degree of node <span +class="cmti-10x-x-109">i </span>on +layer 2. +<!--l. 42--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 42--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 42--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> +<!--l. 42--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 42--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<!--l. 42--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">90</span>, 042807 (2014). +<!--l. 42--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu33.html" >next</a>] [<a +href="mammult_docsu31.html" >prev</a>] [<a +href="mammult_docsu31.html#tailmammult_docsu31.html" >prev-tail</a>] [<a +href="mammult_docsu32.html" >front</a>] [<a +href="mammult_docsu31.html#mammult_docsu32.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu32.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu33.html b/doc/html/mammult_docsu33.html new file mode 100644 index 0000000..d9b78dd --- /dev/null +++ b/doc/html/mammult_docsu33.html @@ -0,0 +1,233 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.3.0 knn_q_from_layers.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu34.html" >next</a>] [<a +href="mammult_docsu32.html" >prev</a>] [<a +href="mammult_docsu32.html#tailmammult_docsu32.html" >prev-tail</a>] [<a +href="#tailmammult_docsu33.html">tail</a>] [<a +href="mammult_docsu31.html#mammult_docsu33.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x37-360001.2.3"></a><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_layers.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">knn</span><span +class="cmbx-10x-x-109">_q</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_layers.py </span>- compute intra-layer and inter-layer degree-degree +correlation coefficients. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">knn</span><span +class="cmbx-10x-x-109">_q</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_layers.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">></span> +<!--l. 43--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 43--><p class="indent" > Compute the intra-layer and the inter-layer degree correlation functions for +two layers given as input. The intra-layer degree correlation function quantifies +the presence of degree-degree correlations in a single layer network, and is defined +as: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc6x.png" alt=" --1- ∑ ′ ′ +⟨knn(k)⟩ = kNk k P(k |k ) + k′ +" class="math-display" ></center></td></tr></table> +<!--l. 43--><p class="nopar" > +<!--l. 43--><p class="indent" > where <span +class="cmmi-10x-x-109">P</span>(<span +class="cmmi-10x-x-109">k</span><span +class="cmsy-10x-x-109">′|</span><span +class="cmmi-10x-x-109">k</span>) is the probability that a neighbour of a node with degree <span +class="cmmi-10x-x-109">k </span>has +degree <span +class="cmmi-10x-x-109">k</span><span +class="cmsy-10x-x-109">′</span>, and <span +class="cmmi-10x-x-109">N</span><sub><span +class="cmmi-8">k</span></sub> is the number of nodes with degree <span +class="cmmi-10x-x-109">k</span>. The quantity <span +class="cmsy-10x-x-109">⟨</span><span +class="cmmi-10x-x-109">k</span><sub><span +class="cmmi-8">nn</span></sub>(<span +class="cmmi-10x-x-109">k</span>)<span +class="cmsy-10x-x-109">⟩ </span>is +the average degree of the neighbours of nodes having degree equal to +<span +class="cmmi-10x-x-109">k</span>. +<!--l. 43--><p class="indent" > If we consider two layers of a multiplex, and we denote by <span +class="cmmi-10x-x-109">k </span>the degree +of a node on the first layer and by <span +class="cmmi-10x-x-109">q </span>the degree of the same node on +the second layers, the inter-layer degree correlation function is defined +as + <table +class="equation-star"><tr><td> + + + + <center class="math-display" > +<img +src="mammult_doc7x.png" alt="-- ∑ ′ ′ +k(q) = k P(k |q) + k′ +" class="math-display" ></center></td></tr></table> +<!--l. 43--><p class="nopar" > +<!--l. 43--><p class="indent" > where <span +class="cmmi-10x-x-109">P</span>(<span +class="cmmi-10x-x-109">k</span><span +class="cmsy-10x-x-109">′|</span><span +class="cmmi-10x-x-109">q</span>) is the probability that a node with degree <span +class="cmmi-10x-x-109">q </span>on the second layer +has degree equal to <span +class="cmmi-10x-x-109">k</span><span +class="cmsy-10x-x-109">′ </span>on the first layer, and <span +class="cmmi-10x-x-109">N</span><sub><span +class="cmmi-8">q</span></sub> is the number of nodes +with degree <span +class="cmmi-10x-x-109">q </span>on the second layer. The quantity <span class="overline"><span +class="cmmi-10x-x-109">k</span></span>(<span +class="cmmi-10x-x-109">q</span>) is the expected +degree at layer 1 of node that have degree equal to <span +class="cmmi-10x-x-109">q </span>on layer 2. The dual +quantity: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc8x.png" alt="-- ∑ ′ ′ +q(k) = q P(q |k) + q′ +" class="math-display" ></center></td></tr></table> +<!--l. 43--><p class="nopar" > +<!--l. 43--><p class="indent" > is the average degree on layer 2 of nodes having degree <span +class="cmmi-10x-x-109">k </span>on layer +1. +<!--l. 73--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 73--><p class="indent" > The program creates two output files, respectively called +<!--l. 73--><p class="indent" >   <span +class="cmti-10x-x-109">file1</span><span +class="cmti-10x-x-109">_file2</span><span +class="cmti-10x-x-109">_k1</span> +<!--l. 73--><p class="indent" > and +<!--l. 73--><p class="indent" >   <span +class="cmti-10x-x-109">file1</span><span +class="cmti-10x-x-109">_file2</span><span +class="cmti-10x-x-109">_k2</span> +<!--l. 73--><p class="indent" > The first file contains a list of lines in the format: +<!--l. 73--><p class="indent" >   <span +class="cmti-10x-x-109">k </span><span +class="cmsy-10x-x-109">⟨</span><span +class="cmmi-10x-x-109">k</span><sub><span +class="cmmi-8">nn</span></sub>(<span +class="cmmi-10x-x-109">k</span>)<span +class="cmsy-10x-x-109">⟩ </span><span +class="cmmi-10x-x-109">σ</span><sub><span +class="cmmi-8">k</span></sub> <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) <span +class="cmmi-10x-x-109">σ</span><sub><span class="overline"><span +class="cmmi-10x-x-109">q</span></span></sub> +<!--l. 73--><p class="indent" > where <span +class="cmmi-10x-x-109">k </span>is the degree at first layer, <span +class="cmsy-10x-x-109">⟨</span><span +class="cmmi-10x-x-109">k</span><sub><span +class="cmmi-8">nn</span></sub>(<span +class="cmmi-10x-x-109">k</span>)<span +class="cmsy-10x-x-109">⟩ </span>is the average degree of the +neighbours at layer 1 of nodes having degree <span +class="cmmi-10x-x-109">k </span>at layer 1, <span +class="cmmi-10x-x-109">σ</span><sub><span +class="cmmi-8">k</span></sub> is the standard +deviation associated to <span +class="cmsy-10x-x-109">⟨</span><span +class="cmmi-10x-x-109">k</span><sub><span +class="cmmi-8">nn</span></sub>(<span +class="cmmi-10x-x-109">k</span>)<span +class="cmsy-10x-x-109">⟩</span>, <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) is the average degree at layer 2 of nodes + + + +having degree equal to <span +class="cmmi-10x-x-109">k </span>at layer 1, and <span +class="cmmi-10x-x-109">σ</span><sub><span class="overline"><span +class="cmmi-10x-x-109">q</span></span></sub> is the standard deviation associated +to <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>). +<!--l. 73--><p class="indent" > The second file contains a similar list of lines, in the format: +<!--l. 73--><p class="indent" >   <span +class="cmti-10x-x-109">q </span><span +class="cmsy-10x-x-109">⟨</span><span +class="cmmi-10x-x-109">q</span><sub><span +class="cmmi-8">nn</span></sub>(<span +class="cmmi-10x-x-109">q</span>)<span +class="cmsy-10x-x-109">⟩ </span><span +class="cmmi-10x-x-109">σ</span><sub><span +class="cmmi-8">q</span></sub> <span class="overline"><span +class="cmmi-10x-x-109">k</span></span>(<span +class="cmmi-10x-x-109">q</span>) <span +class="cmmi-10x-x-109">σ</span><sub><span class="overline"><span +class="cmmi-10x-x-109">k</span></span></sub> +<!--l. 73--><p class="indent" > with obvious meaning. +<!--l. 80--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 80--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 80--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> +<!--l. 80--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 80--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<!--l. 80--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">90</span>, 042807 (2014). +<!--l. 80--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu34.html" >next</a>] [<a +href="mammult_docsu32.html" >prev</a>] [<a +href="mammult_docsu32.html#tailmammult_docsu32.html" >prev-tail</a>] [<a +href="mammult_docsu33.html" >front</a>] [<a +href="mammult_docsu31.html#mammult_docsu33.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu33.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu34.html b/doc/html/mammult_docsu34.html new file mode 100644 index 0000000..ccd8b5a --- /dev/null +++ b/doc/html/mammult_docsu34.html @@ -0,0 +1,164 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.3.0 knn_q_from_degrees.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu35.html" >next</a>] [<a +href="mammult_docsu33.html" >prev</a>] [<a +href="mammult_docsu33.html#tailmammult_docsu33.html" >prev-tail</a>] [<a +href="#tailmammult_docsu34.html">tail</a>] [<a +href="mammult_docsu31.html#mammult_docsu34.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x38-370001.2.3"></a><span +class="cmtt-10x-x-109">knn</span><span +class="cmtt-10x-x-109">_q</span><span +class="cmtt-10x-x-109">_from</span><span +class="cmtt-10x-x-109">_degrees.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">knn</span><span +class="cmbx-10x-x-109">_q</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_degrees.py </span>- compute the inter-layer degree-degree +correlation function. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">knn</span><span +class="cmbx-10x-x-109">_q</span><span +class="cmbx-10x-x-109">_from</span><span +class="cmbx-10x-x-109">_degrees.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">filein</span><span +class="cmmi-10x-x-109">></span> +<!--l. 37--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 37--><p class="indent" > Compute the inter-layer degree correlation functions for two layers of a +multiplex, using the degrees of the nodes specified in the input file. The format of +the input file is as follows +<!--l. 37--><p class="indent" >   <span +class="cmti-10x-x-109">ki qi</span> +<!--l. 37--><p class="indent" > where <span +class="cmti-10x-x-109">ki </span>and <span +class="cmti-10x-x-109">qi </span>are, respectively, the degree at layer 1 and the degree at layer +2 of node <span +class="cmti-10x-x-109">i</span>. +<!--l. 37--><p class="indent" > If we consider two layers of a multiplex, and we denote by <span +class="cmmi-10x-x-109">k </span>the degree +of a node on the first layer and by <span +class="cmmi-10x-x-109">q </span>the degree of the same node on +the second layers, the inter-layer degree correlation function is defined +as + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc9x.png" alt="k(q) = -1-∑ k′P (k′|q) + Nk ′ + k +" class="math-display" ></center></td></tr></table> +<!--l. 37--><p class="nopar" > +<!--l. 37--><p class="indent" > where <span +class="cmmi-10x-x-109">P</span>(<span +class="cmmi-10x-x-109">k</span><span +class="cmsy-10x-x-109">′|</span><span +class="cmmi-10x-x-109">q</span>) is the probability that a node with degree <span +class="cmmi-10x-x-109">q </span>on the second +layer has degree equal to <span +class="cmmi-10x-x-109">k</span><span +class="cmsy-10x-x-109">′ </span>on the first layer, and <span +class="cmmi-10x-x-109">N</span><sub><span +class="cmmi-8">k</span></sub> is the number of +nodes with degree <span +class="cmmi-10x-x-109">k </span>on the first layer. The quantity <span class="overline"><span +class="cmmi-10x-x-109">k</span></span>(<span +class="cmmi-10x-x-109">q</span>) is the expected +degree at layer 1 of node that have degree equal to <span +class="cmmi-10x-x-109">q </span>on layer 2. The dual + + + +quantity: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc10x.png" alt=" ∑ +q(k) = -1- q′P (q′|k) + Nq q′ +" class="math-display" ></center></td></tr></table> +<!--l. 37--><p class="nopar" > +<!--l. 37--><p class="indent" > is the average degree on layer 2 of nodes having degree <span +class="cmmi-10x-x-109">k </span>on layer +1. +<!--l. 57--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 57--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: +<!--l. 57--><p class="indent" >   <span +class="cmti-10x-x-109">k </span><span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) +<!--l. 57--><p class="indent" > where <span +class="cmti-10x-x-109">k </span>is the degree on layer 1 and <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) is the average degree on layer 2 of +nodes having degree equal to <span +class="cmmi-10x-x-109">k </span>on layer 1. +<!--l. 57--><p class="indent" > The program also prints on <span +class="cmtt-10x-x-109">stderr </span>a list of lines in the format: +<!--l. 57--><p class="indent" >   <span +class="cmti-10x-x-109">q </span><span class="overline"><span +class="cmmi-10x-x-109">k</span></span>(<span +class="cmmi-10x-x-109">q</span>) +<!--l. 57--><p class="indent" > where <span +class="cmti-10x-x-109">q </span>is the degree on layer 2 and <span class="overline"><span +class="cmmi-10x-x-109">k</span></span>(<span +class="cmmi-10x-x-109">q</span>) is the average degree on layer 1 of +nodes having degree equal to <span +class="cmmi-10x-x-109">q </span>on layer 2. +<!--l. 64--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 64--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 64--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> +<!--l. 64--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 64--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<!--l. 64--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">90</span>, 042807 (2014). +<!--l. 64--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a> + + + + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu35.html" >next</a>] [<a +href="mammult_docsu33.html" >prev</a>] [<a +href="mammult_docsu33.html#tailmammult_docsu33.html" >prev-tail</a>] [<a +href="mammult_docsu34.html" >front</a>] [<a +href="mammult_docsu31.html#mammult_docsu34.html" >up</a>] </p></div> +<!--l. 4--><p class="indent" > <a + id="tailmammult_docsu34.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu35.html b/doc/html/mammult_docsu35.html new file mode 100644 index 0000000..7bac046 --- /dev/null +++ b/doc/html/mammult_docsu35.html @@ -0,0 +1,140 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.2.3.0 fit_knn</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docch2.html" >next</a>] [<a +href="mammult_docsu34.html" >prev</a>] [<a +href="mammult_docsu34.html#tailmammult_docsu34.html" >prev-tail</a>] [<a +href="#tailmammult_docsu35.html">tail</a>] [<a +href="mammult_docsu31.html#mammult_docsu35.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x39-380001.2.3"></a><span +class="cmtt-10x-x-109">fit</span><span +class="cmtt-10x-x-109">_knn</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">fit</span><span +class="cmbx-10x-x-109">_knn </span>- power-law fit of the inter-layer degree correlation function. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">fit</span><span +class="cmbx-10x-x-109">_knn </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">filein</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">alpha</span><span +class="cmmi-10x-x-109">></span> +<!--l. 37--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 37--><p class="indent" > Perform a power-law fit of the inter-layer degree correlation function: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc11x.png" alt="-- 1 ∑ +q(k) = --- q′P (q′|k) + Nq q′ +" class="math-display" ></center></td></tr></table> +<!--l. 37--><p class="nopar" > +<!--l. 37--><p class="indent" > where <span +class="cmmi-10x-x-109">k </span>is the degree of a node on layer 1, <span +class="cmmi-10x-x-109">q </span>is the degree on layer 2 and +<span +class="cmmi-10x-x-109">P</span>(<span +class="cmmi-10x-x-109">q</span><span +class="cmsy-10x-x-109">|</span><span +class="cmmi-10x-x-109">k</span>) is the probability that a node with degree <span +class="cmmi-10x-x-109">k </span>on layer 1 has degree <span +class="cmmi-10x-x-109">q </span>on +layer 2. The program assumes that <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) can be written in the form <span +class="cmmi-10x-x-109">ak</span><sup><span +class="cmmi-8">b</span></sup>, and +computes the two parameters <span +class="cmmi-10x-x-109">a </span>and <span +class="cmmi-10x-x-109">b </span>through a linear fit of the log-log plot of +<span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>). +<!--l. 37--><p class="indent" > The input file <span +class="cmti-10x-x-109">filein </span>contains a list of lines in the format: +<!--l. 37--><p class="indent" >   <span +class="cmti-10x-x-109">ki qi</span> +<!--l. 37--><p class="indent" > where <span +class="cmti-10x-x-109">ki </span>is the degree of node <span +class="cmmi-10x-x-109">i </span>at layer 1 and <span +class="cmti-10x-x-109">qi </span>is the degree of node <span +class="cmmi-10x-x-109">i </span>at +layer 2. +<!--l. 37--><p class="indent" > The second parameter <span +class="cmti-10x-x-109">alpha </span>is the ratio of the progression used to generate +the exponentially-distributed bins for the log-log plot. Typical values of <span +class="cmti-10x-x-109">alpha </span>are +between 1<span +class="cmmi-10x-x-109">.</span>1 and 2<span +class="cmmi-10x-x-109">.</span>0. +<!--l. 37--><p class="indent" > N.B.: The exponent <span +class="cmmi-10x-x-109">b </span>computed with this method is known to be +inaccurate. + + + +<!--l. 43--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 43--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>the values of the parameters <span +class="cmmi-10x-x-109">a </span>and <span +class="cmmi-10x-x-109">b </span>of the +power-law fit <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) = <span +class="cmmi-10x-x-109">ak</span><sup><span +class="cmmi-8">b</span></sup>. +<!--l. 50--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 50--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 50--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> +<!--l. 50--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 50--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<!--l. 50--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">90</span>, 042807 (2014). +<!--l. 50--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a> + + + + <!--l. 208--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docch2.html" >next</a>] [<a +href="mammult_docsu34.html" >prev</a>] [<a +href="mammult_docsu34.html#tailmammult_docsu34.html" >prev-tail</a>] [<a +href="mammult_docsu35.html" >front</a>] [<a +href="mammult_docsu31.html#mammult_docsu35.html" >up</a>] </p></div> +<!--l. 208--><p class="indent" > <a + id="tailmammult_docsu35.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu36.html b/doc/html/mammult_docsu36.html new file mode 100644 index 0000000..a1f0f0f --- /dev/null +++ b/doc/html/mammult_docsu36.html @@ -0,0 +1,56 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Null-models of node and layer activity</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 212--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu37.html" >next</a>] [<a +href="mammult_docse3.html" >prev</a>] [<a +href="mammult_docse3.html#tailmammult_docse3.html" >prev-tail</a>] [<a +href="#tailmammult_docsu36.html">tail</a>] [<a +href="mammult_docse3.html#mammult_docsu36.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">2.1.1 </span> <a + id="x42-410002.1.1"></a>Null-models of node and layer activity</h4> +<!--l. 3--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu37.html#x43-420002.1.1"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_hypergeometric.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu38.html#x44-430002.1.1"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_MDM.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu39.html#x45-440002.1.1"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_MSM.py</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu40.html#x46-450002.1.1"><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_layer</span><span +class="cmtt-10x-x-109">_growth.py</span></a></span> + </div> + + + + + + + <!--l. 220--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu37.html" >next</a>] [<a +href="mammult_docse3.html" >prev</a>] [<a +href="mammult_docse3.html#tailmammult_docse3.html" >prev-tail</a>] [<a +href="mammult_docsu36.html" >front</a>] [<a +href="mammult_docse3.html#mammult_docsu36.html" >up</a>] </p></div> +<!--l. 220--><p class="indent" > <a + id="tailmammult_docsu36.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu37.html b/doc/html/mammult_docsu37.html new file mode 100644 index 0000000..7f93983 --- /dev/null +++ b/doc/html/mammult_docsu37.html @@ -0,0 +1,98 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.1.1.0 model_hypergeometric.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu38.html" >next</a>] [<a +href="mammult_docsu36.html" >prev</a>] [<a +href="mammult_docsu36.html#tailmammult_docsu36.html" >prev-tail</a>] [<a +href="#tailmammult_docsu37.html">tail</a>] [<a +href="mammult_docsu36.html#mammult_docsu37.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x43-420002.1.1"></a><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_hypergeometric.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">model</span><span +class="cmbx-10x-x-109">_hypergeometric.py </span>- Hypergeometric node activity null +model. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">model</span><span +class="cmbx-10x-x-109">_hypergeometric.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer</span><span +class="cmitt-10x-x-109">_N</span><span +class="cmitt-10x-x-109">_file</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">></span> +<!--l. 15--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 15--><p class="indent" > This is the hypergeometric model of node activation. In this model each layer +has exactly the same number of active node of a reference multiplex network, but +nodes on each layer are activated uniformly at random, thus destroying all +inter-layer activity correlation patterns. +<!--l. 15--><p class="indent" > The file <span +class="cmti-10x-x-109">layer</span><span +class="cmti-10x-x-109">_N</span><span +class="cmti-10x-x-109">_file </span>reports on the n-th line the number of active nodes on +the n-th layer (starting from zero). The second parameter <span +class="cmti-10x-x-109">N </span>is the total number +of active nodes in the multiplex. +<!--l. 31--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 31--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a node-layer list of lines in the format: +<!--l. 31--><p class="indent" >   <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i layer</span><span +class="cmti-10x-x-109">_i</span> +<!--l. 31--><p class="indent" > where <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i </span>is the ID of a node and <span +class="cmti-10x-x-109">layre</span><span +class="cmti-10x-x-109">_i </span>is the ID of a layer. This +list indicates which nodes are active in which layer. For instance, the +line: +<!--l. 31--><p class="indent" >   <span +class="cmti-10x-x-109">24 3</span> +<!--l. 31--><p class="indent" > indicates that the node with ID <span +class="cmti-10x-x-109">24 </span>is active on layer <span +class="cmti-10x-x-109">3</span>. +<!--l. 33--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 33--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 33--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu38.html" >next</a>] [<a +href="mammult_docsu36.html" >prev</a>] [<a +href="mammult_docsu36.html#tailmammult_docsu36.html" >prev-tail</a>] [<a +href="mammult_docsu37.html" >front</a>] [<a +href="mammult_docsu36.html#mammult_docsu37.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu37.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu38.html b/doc/html/mammult_docsu38.html new file mode 100644 index 0000000..1f1e918 --- /dev/null +++ b/doc/html/mammult_docsu38.html @@ -0,0 +1,106 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.1.1.0 model_MDM.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu39.html" >next</a>] [<a +href="mammult_docsu37.html" >prev</a>] [<a +href="mammult_docsu37.html#tailmammult_docsu37.html" >prev-tail</a>] [<a +href="#tailmammult_docsu38.html">tail</a>] [<a +href="mammult_docsu36.html#mammult_docsu38.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x44-430002.1.1"></a><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_MDM.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">model</span><span +class="cmbx-10x-x-109">_MDM.py </span>- Multi-activity Deterministic Model. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">model</span><span +class="cmbx-10x-x-109">_MDM.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">Bi</span><span +class="cmitt-10x-x-109">_file</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">M</span><span +class="cmmi-10x-x-109">></span> +<!--l. 23--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 23--><p class="indent" > This is the Multi-activity Deterministic Model (MDM). In this model each +node <span +class="cmmi-10x-x-109">i </span>is considered active if it was active in the reference multiplex, maintains +the same value of node activity <span +class="cmmi-10x-x-109">B</span><sub><span +class="cmmi-8">i</span></sub> (i.e., the number of layers in which it was +active) and is associated an activity vector sampled uniformly at random from +the <span +class="cmex-10x-x-109">(</span><span +class="cmmi-8">M</span> + <span +class="cmmi-8">B</span><sub><span +class="cmmi-6">i</span></sub><span +class="cmex-10x-x-109">)</span> + possible activity vectors with <span +class="cmmi-10x-x-109">B</span><sub><span +class="cmmi-8">i</span></sub> non-null entries. +<!--l. 23--><p class="indent" > The file <span +class="cmti-10x-x-109">Bi</span><span +class="cmti-10x-x-109">_file </span>is in the format: +<!--l. 23--><p class="indent" >   <span +class="cmti-10x-x-109">Bi N(Bi)</span> +<!--l. 23--><p class="indent" > where <span +class="cmti-10x-x-109">Bi </span>is a value of node activity and <span +class="cmti-10x-x-109">N(Bi) </span>is the number of nodes which +had node activity equaly to <span +class="cmti-10x-x-109">Bi </span>in the reference multiplex. +<!--l. 23--><p class="indent" > The parameter <span +class="cmti-10x-x-109">M </span>is the number of layers in the multiplex. +<!--l. 34--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 34--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a distribution of bit-strings, in the +format: +<!--l. 34--><p class="indent" >   <span +class="cmti-10x-x-109">Bi bitstring count</span> +<!--l. 34--><p class="indent" > where <span +class="cmti-10x-x-109">bitstring </span>is the activity bitstring, <span +class="cmti-10x-x-109">Bi </span>is the number of non-zero entries +of <span +class="cmti-10x-x-109">bitstring </span>and <span +class="cmti-10x-x-109">count </span>is the number of times that <span +class="cmti-10x-x-109">bitstrings </span>appear in the null +model. +<!--l. 37--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 37--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 37--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu39.html" >next</a>] [<a +href="mammult_docsu37.html" >prev</a>] [<a +href="mammult_docsu37.html#tailmammult_docsu37.html" >prev-tail</a>] [<a +href="mammult_docsu38.html" >front</a>] [<a +href="mammult_docsu36.html#mammult_docsu38.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu38.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu39.html b/doc/html/mammult_docsu39.html new file mode 100644 index 0000000..a372150 --- /dev/null +++ b/doc/html/mammult_docsu39.html @@ -0,0 +1,107 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.1.1.0 model_MSM.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu40.html" >next</a>] [<a +href="mammult_docsu38.html" >prev</a>] [<a +href="mammult_docsu38.html#tailmammult_docsu38.html" >prev-tail</a>] [<a +href="#tailmammult_docsu39.html">tail</a>] [<a +href="mammult_docsu36.html#mammult_docsu39.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x45-440002.1.1"></a><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_MSM.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">model</span><span +class="cmbx-10x-x-109">_MSM.py </span>- Multi-activity Stochastic Model. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">model</span><span +class="cmbx-10x-x-109">_MSM.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">node</span><span +class="cmitt-10x-x-109">_Bi</span><span +class="cmitt-10x-x-109">_file</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">M</span><span +class="cmmi-10x-x-109">></span> +<!--l. 21--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 21--><p class="indent" > This is the Multi-activity Stochastic Model (MSM). In this model each node <span +class="cmmi-10x-x-109">i</span> +is considered active if it was active in the reference multiplex, and is activated on +each layer with a probability equal to <span +class="cmmi-10x-x-109">B</span><sub><span +class="cmmi-8">i</span></sub><span +class="cmmi-10x-x-109">∕M </span>where <span +class="cmmi-10x-x-109">B</span><sub><span +class="cmmi-8">i</span></sub> was the activity of node <span +class="cmmi-10x-x-109">i</span> +in the reference multiplex. +<!--l. 21--><p class="indent" > The file <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_Bi</span><span +class="cmti-10x-x-109">_file </span>is in the format: +<!--l. 21--><p class="indent" >   <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i Bi)</span> +<!--l. 21--><p class="indent" > where <span +class="cmti-10x-x-109">Bi </span>is the value of node activity of <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i </span>in the reference multiplex. +<!--l. 21--><p class="indent" > The parameter <span +class="cmti-10x-x-109">M </span>is the number of layers in the multiplex. +<!--l. 36--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 36--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a node-layer list of lines in the format: +<!--l. 36--><p class="indent" >   <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i layer</span><span +class="cmti-10x-x-109">_i</span> +<!--l. 36--><p class="indent" > where <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i </span>is the ID of a node and <span +class="cmti-10x-x-109">layre</span><span +class="cmti-10x-x-109">_i </span>is the ID of a layer. This +list indicates which nodes are active in which layer. For instance, the +line: +<!--l. 36--><p class="indent" >   <span +class="cmti-10x-x-109">24 3</span> +<!--l. 36--><p class="indent" > indicates that the node with ID <span +class="cmti-10x-x-109">24 </span>is active on layer <span +class="cmti-10x-x-109">3</span>. +<!--l. 38--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 38--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 38--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu40.html" >next</a>] [<a +href="mammult_docsu38.html" >prev</a>] [<a +href="mammult_docsu38.html#tailmammult_docsu38.html" >prev-tail</a>] [<a +href="mammult_docsu39.html" >front</a>] [<a +href="mammult_docsu36.html#mammult_docsu39.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu39.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu4.html b/doc/html/mammult_docsu4.html new file mode 100644 index 0000000..bfd3aa7 --- /dev/null +++ b/doc/html/mammult_docsu4.html @@ -0,0 +1,96 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 node_activity_vectors.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu5.html" >next</a>] [<a +href="mammult_docsu3.html" >prev</a>] [<a +href="mammult_docsu3.html#tailmammult_docsu3.html" >prev-tail</a>] [<a +href="#tailmammult_docsu4.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu4.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x7-60001.1.1"></a><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_vectors.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">node</span><span +class="cmbx-10x-x-109">_activity</span><span +class="cmbx-10x-x-109">_vectors.py </span>- compute the activity vectors of all the nodes of +a multiplex. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">node</span><span +class="cmbx-10x-x-109">_activity</span><span +class="cmbx-10x-x-109">_vectors.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 15--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 15--><p class="indent" > Compute and print on output the activity vectors of the nodes of a +multiplex network, whose layers are given as input in the files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, +etc. +<!--l. 15--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 15--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 15--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 26--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 26--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains +the activity vector of the n-th node, i.e. a bit-string where each bit is +set to “1” if the node is active on the corresponding layer, and to “0” +otherwise. +<!--l. 26--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if +a node ID is not present in any of the layer files given as input, the program +considers it as being isolated on all the layers, and will print on output a +bit-string of zeros. +<!--l. 28--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 28--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 28--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu5.html" >next</a>] [<a +href="mammult_docsu3.html" >prev</a>] [<a +href="mammult_docsu3.html#tailmammult_docsu3.html" >prev-tail</a>] [<a +href="mammult_docsu4.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu4.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu4.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu40.html b/doc/html/mammult_docsu40.html new file mode 100644 index 0000000..5edece7 --- /dev/null +++ b/doc/html/mammult_docsu40.html @@ -0,0 +1,138 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.1.1.0 model_layer_growth.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse4.html" >next</a>] [<a +href="mammult_docsu39.html" >prev</a>] [<a +href="mammult_docsu39.html#tailmammult_docsu39.html" >prev-tail</a>] [<a +href="#tailmammult_docsu40.html">tail</a>] [<a +href="mammult_docsu36.html#mammult_docsu40.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x46-450002.1.1"></a><span +class="cmtt-10x-x-109">model</span><span +class="cmtt-10x-x-109">_layer</span><span +class="cmtt-10x-x-109">_growth.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">model</span><span +class="cmbx-10x-x-109">_layer</span><span +class="cmbx-10x-x-109">_growth.py </span>- Layer growth with preferential activation +model. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">model</span><span +class="cmbx-10x-x-109">_layer</span><span +class="cmbx-10x-x-109">_growth.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer</span><span +class="cmitt-10x-x-109">_N</span><span +class="cmitt-10x-x-109">_file</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">M0</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">A</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmitt-10x-x-109">[RND]</span> +<!--l. 29--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 29--><p class="indent" > This is the model of layer growth with preferential node activation. In this +model an entire new layer arrives at time <span +class="cmmi-10x-x-109">t </span>and a number of nodes <span +class="cmmi-10x-x-109">N</span><sub><span +class="cmmi-8">t</span></sub> is +activated (<span +class="cmmi-10x-x-109">N</span>_<span +class="cmmi-10x-x-109">t </span>is equal to the number of nodes active on that layer in the +reference multiplex). Then, each node <span +class="cmmi-10x-x-109">i </span>of the new layer is activated with a +probability: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc12x.png" alt="Pi(t) ∝ A + Bi (t) +" class="math-display" ></center></td></tr></table> +<!--l. 29--><p class="nopar" > +<!--l. 29--><p class="indent" > where <span +class="cmmi-10x-x-109">B</span><sub><span +class="cmmi-8">i</span></sub>(<span +class="cmmi-10x-x-109">t</span>) is the activity of node <span +class="cmmi-10x-x-109">i </span>at time <span +class="cmmi-10x-x-109">t </span>(i.e., the number of +layers in which node <span +class="cmmi-10x-x-109">i </span>is active at time <span +class="cmmi-10x-x-109">t</span>) while <span +class="cmmi-10x-x-109">A > </span>0 is an intrinsic +attractiveness. +<!--l. 29--><p class="indent" > The file <span +class="cmti-10x-x-109">layer</span><span +class="cmti-10x-x-109">_N</span><span +class="cmti-10x-x-109">_file </span>reports on the n-th line the number of active nodes on +the n-th layer. +<!--l. 29--><p class="indent" > The parameter <span +class="cmti-10x-x-109">N </span>is the number of nodes in the multiplex, <span +class="cmti-10x-x-109">M0 </span>is the number +of layers in the initial network, <span +class="cmti-10x-x-109">A </span>is the value of node attractiveness. +<!--l. 29--><p class="indent" > If the user specifies <span +class="cmtt-10x-x-109">RND </span>as the last parameter, the sequence of layers +is + + + +<!--l. 44--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 44--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a node-layer list of lines in the format: +<!--l. 44--><p class="indent" >   <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i layer</span><span +class="cmti-10x-x-109">_i</span> +<!--l. 44--><p class="indent" > where <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i </span>is the ID of a node and <span +class="cmti-10x-x-109">layre</span><span +class="cmti-10x-x-109">_i </span>is the ID of a layer. This +list indicates which nodes are active in which layer. For instance, the +line: +<!--l. 44--><p class="indent" >   <span +class="cmti-10x-x-109">24 3</span> +<!--l. 44--><p class="indent" > indicates that the node with ID <span +class="cmti-10x-x-109">24 </span>is active on layer <span +class="cmti-10x-x-109">3</span>. +<!--l. 46--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 46--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 46--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 220--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse4.html" >next</a>] [<a +href="mammult_docsu39.html" >prev</a>] [<a +href="mammult_docsu39.html#tailmammult_docsu39.html" >prev-tail</a>] [<a +href="mammult_docsu40.html" >front</a>] [<a +href="mammult_docsu36.html#mammult_docsu40.html" >up</a>] </p></div> +<!--l. 220--><p class="indent" > <a + id="tailmammult_docsu40.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu41.html b/doc/html/mammult_docsu41.html new file mode 100644 index 0000000..babf303 --- /dev/null +++ b/doc/html/mammult_docsu41.html @@ -0,0 +1,61 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Linear preferential attachment</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 222--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu42.html" >next</a>] [<a +href="mammult_docse4.html" >prev</a>] [<a +href="mammult_docse4.html#tailmammult_docse4.html" >prev-tail</a>] [<a +href="#tailmammult_docsu41.html">tail</a>] [<a +href="mammult_docse4.html#mammult_docsu41.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">2.2.1 </span> <a + id="x48-470002.2.1"></a>Linear preferential attachment</h4> +<!--l. 4--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu42.html#x49-480002.2.1"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delta</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu43.html#x50-490002.2.1"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delay</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu44.html#x51-500002.2.1"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delay</span><span +class="cmtt-10x-x-109">_mix</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu45.html#x52-510002.2.1"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_random</span><span +class="cmtt-10x-x-109">_times</span></a></span> + </div> + + + + + + + <!--l. 230--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu42.html" >next</a>] [<a +href="mammult_docse4.html" >prev</a>] [<a +href="mammult_docse4.html#tailmammult_docse4.html" >prev-tail</a>] [<a +href="mammult_docsu41.html" >front</a>] [<a +href="mammult_docse4.html#mammult_docsu41.html" >up</a>] </p></div> +<!--l. 230--><p class="indent" > <a + id="tailmammult_docsu41.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu42.html b/doc/html/mammult_docsu42.html new file mode 100644 index 0000000..5727bf0 --- /dev/null +++ b/doc/html/mammult_docsu42.html @@ -0,0 +1,145 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.2.1.0 nibilab_linear_delta</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu43.html" >next</a>] [<a +href="mammult_docsu41.html" >prev</a>] [<a +href="mammult_docsu41.html#tailmammult_docsu41.html" >prev-tail</a>] [<a +href="#tailmammult_docsu42.html">tail</a>] [<a +href="mammult_docsu41.html#mammult_docsu42.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x49-480002.2.1"></a><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delta</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_linear</span><span +class="cmbx-10x-x-109">_delta </span>- Multiplex linear preferential attachment model – +Synchronous arrival. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> + + + +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_linear</span><span +class="cmbx-10x-x-109">_delta </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m0</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">outfile</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">a</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">b</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">c</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">d</span><span +class="cmmi-10x-x-109">></span> +<!--l. 44--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 44--><p class="indent" > Grow a two-layer multiplex network using the multiplex linear preferential +attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB). +<!--l. 44--><p class="indent" > The probability for a newly arrived node <span +class="cmmi-10x-x-109">i </span>to create a link to node <span +class="cmmi-10x-x-109">j </span>on layer +1 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc13x.png" alt="Π1i→j ∝ ak[1j]+ bk[j2] +" class="math-display" ></center></td></tr></table> +<!--l. 44--><p class="nopar" > +<!--l. 44--><p class="indent" > and the dual probability for <span +class="cmmi-10x-x-109">i </span>to create a link to <span +class="cmmi-10x-x-109">j </span>on layer 2 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc14x.png" alt="Π2 ∝ ck [1]+ dk[2] + i→j j j +" class="math-display" ></center></td></tr></table> +<!--l. 44--><p class="nopar" > +<!--l. 44--><p class="indent" > Each new node arrives at the same time on both layers. +<!--l. 44--><p class="indent" > The (mandatory) parameters are as follows: + <ul class="itemize1"> + <li class="itemize"><span +class="cmbx-10x-x-109">N </span>number of nodes in the final graph + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m </span>number of new edges brought by each new node + + + + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span +class="cmti-10x-x-109">m0 </span>must be larger than + of equal to <span +class="cmti-10x-x-109">m</span>. + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function + </li></ul> +<!--l. 55--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 55--><p class="indent" > The program dumps on the file <span +class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the +resulting network. Each line of the file is in the format: +<!--l. 55--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 55--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 57--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 57--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 57--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> + + + + <!--l. 5--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu43.html" >next</a>] [<a +href="mammult_docsu41.html" >prev</a>] [<a +href="mammult_docsu41.html#tailmammult_docsu41.html" >prev-tail</a>] [<a +href="mammult_docsu42.html" >front</a>] [<a +href="mammult_docsu41.html#mammult_docsu42.html" >up</a>] </p></div> +<!--l. 5--><p class="indent" > <a + id="tailmammult_docsu42.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu43.html b/doc/html/mammult_docsu43.html new file mode 100644 index 0000000..d88d970 --- /dev/null +++ b/doc/html/mammult_docsu43.html @@ -0,0 +1,158 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.2.1.0 nibilab_linear_delay</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 5--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu44.html" >next</a>] [<a +href="mammult_docsu42.html" >prev</a>] [<a +href="mammult_docsu42.html#tailmammult_docsu42.html" >prev-tail</a>] [<a +href="#tailmammult_docsu43.html">tail</a>] [<a +href="mammult_docsu41.html#mammult_docsu43.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x50-490002.2.1"></a><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delay</span></h5> +<!--l. 5--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 5--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_linear</span><span +class="cmbx-10x-x-109">_delay </span>- Multiplex linear preferential attachment model – +Asynchronous arrival. +<!--l. 5--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 5--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_linear</span><span +class="cmbx-10x-x-109">_delay </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m0</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">outfile</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">a</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">b</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">c</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">d</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">beta</span><span +class="cmmi-10x-x-109">></span> +<!--l. 54--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 54--><p class="indent" > Grow a two-layer multiplex network using the multiplex linear preferential +attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB). +<!--l. 54--><p class="indent" > The probability for a newly arrived node <span +class="cmmi-10x-x-109">i </span>to create a link to node <span +class="cmmi-10x-x-109">j </span>on layer +1 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc15x.png" alt=" 1 [1] [2] +Π i→j ∝ akj + bkj +" class="math-display" ></center></td></tr></table> +<!--l. 54--><p class="nopar" > +<!--l. 54--><p class="indent" > and the dual probability for <span +class="cmmi-10x-x-109">i </span>to create a link to <span +class="cmmi-10x-x-109">j </span>on layer 2 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc16x.png" alt=" 2 [1] [2] +Π i→j ∝ ck j + dkj +" class="math-display" ></center></td></tr></table> +<!--l. 54--><p class="nopar" > +<!--l. 54--><p class="indent" > Each new node arrives first on layer 1, and its replica on the layer 2 appears +after a time delay <span +class="cmmi-10x-x-109">τ </span>sampled from the power-law function: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc17x.png" alt="P(τ) ∼ τ−β +" class="math-display" ></center></td></tr></table> +<!--l. 54--><p class="nopar" > +<!--l. 54--><p class="indent" > The (mandatory) parameters are as follows: + <ul class="itemize1"> + <li class="itemize"><span +class="cmbx-10x-x-109">N </span>number of nodes in the final graph + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m </span>number of new edges brought by each new node + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span +class="cmti-10x-x-109">m0 </span>must be larger than + of equal to <span +class="cmti-10x-x-109">m</span>. + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">beta </span>the exponent of the power-law delay function which determines + the arrival of replicas on layer 2 + </li></ul> + + + +<!--l. 65--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 65--><p class="indent" > The program dumps on the file <span +class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the +resulting network. Each line of the file is in the format: +<!--l. 65--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 65--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 67--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 67--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 67--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> + + + + <!--l. 5--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu44.html" >next</a>] [<a +href="mammult_docsu42.html" >prev</a>] [<a +href="mammult_docsu42.html#tailmammult_docsu42.html" >prev-tail</a>] [<a +href="mammult_docsu43.html" >front</a>] [<a +href="mammult_docsu41.html#mammult_docsu43.html" >up</a>] </p></div> +<!--l. 5--><p class="indent" > <a + id="tailmammult_docsu43.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu44.html b/doc/html/mammult_docsu44.html new file mode 100644 index 0000000..2303b84 --- /dev/null +++ b/doc/html/mammult_docsu44.html @@ -0,0 +1,163 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.2.1.0 nibilab_linear_delay_mix</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 5--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu45.html" >next</a>] [<a +href="mammult_docsu43.html" >prev</a>] [<a +href="mammult_docsu43.html#tailmammult_docsu43.html" >prev-tail</a>] [<a +href="#tailmammult_docsu44.html">tail</a>] [<a +href="mammult_docsu41.html#mammult_docsu44.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x51-500002.2.1"></a><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_delay</span><span +class="cmtt-10x-x-109">_mix</span></h5> +<!--l. 5--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 5--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_linear</span><span +class="cmbx-10x-x-109">_delay</span><span +class="cmbx-10x-x-109">_mix </span>- Multiplex linear preferential attachment model +– Asynchronous arrival and randomly selected first layer. +<!--l. 5--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 5--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_linear</span><span +class="cmbx-10x-x-109">_delay</span><span +class="cmbx-10x-x-109">_mix </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m0</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">outfile</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">a</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">b</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">c</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">d</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">beta</span><span +class="cmmi-10x-x-109">></span> +<!--l. 55--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 55--><p class="indent" > Grow a two-layer multiplex network using the multiplex linear preferential +attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB). +<!--l. 55--><p class="indent" > The probability for a newly arrived node <span +class="cmmi-10x-x-109">i </span>to create a link to node <span +class="cmmi-10x-x-109">j </span>on layer +1 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc18x.png" alt=" 1 [1] [2] +Π i→j ∝ akj + bkj +" class="math-display" ></center></td></tr></table> +<!--l. 55--><p class="nopar" > +<!--l. 55--><p class="indent" > and the dual probability for <span +class="cmmi-10x-x-109">i </span>to create a link to <span +class="cmmi-10x-x-109">j </span>on layer 2 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc19x.png" alt=" 2 [1] [2] +Π i→j ∝ ck j + dkj +" class="math-display" ></center></td></tr></table> +<!--l. 55--><p class="nopar" > +<!--l. 55--><p class="indent" > Each new node arrives on one of the two layers, chosen uniformly at random, +and its replica on the other layer appears after a time delay <span +class="cmmi-10x-x-109">τ </span>sampled from the +power-law function: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc20x.png" alt=" −β +P(τ) ∼ τ +" class="math-display" ></center></td></tr></table> +<!--l. 55--><p class="nopar" > +<!--l. 55--><p class="indent" > The (mandatory) parameters are as follows: + <ul class="itemize1"> + <li class="itemize"><span +class="cmbx-10x-x-109">N </span>number of nodes in the final graph + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m </span>number of new edges brought by each new node + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span +class="cmti-10x-x-109">m0 </span>must be larger than + of equal to <span +class="cmti-10x-x-109">m</span>. + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">beta </span>the exponent of the power-law delay function which determines + the arrival of replicas on layer 2 + </li></ul> + + + +<!--l. 66--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 66--><p class="indent" > The program dumps on the file <span +class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the +resulting network. Each line of the file is in the format: +<!--l. 66--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 66--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 68--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 68--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 68--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> + + + + <!--l. 6--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu45.html" >next</a>] [<a +href="mammult_docsu43.html" >prev</a>] [<a +href="mammult_docsu43.html#tailmammult_docsu43.html" >prev-tail</a>] [<a +href="mammult_docsu44.html" >front</a>] [<a +href="mammult_docsu41.html#mammult_docsu44.html" >up</a>] </p></div> +<!--l. 6--><p class="indent" > <a + id="tailmammult_docsu44.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu45.html b/doc/html/mammult_docsu45.html new file mode 100644 index 0000000..28adf3f --- /dev/null +++ b/doc/html/mammult_docsu45.html @@ -0,0 +1,146 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.2.1.0 nibilab_linear_random_times</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 6--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu46.html" >next</a>] [<a +href="mammult_docsu44.html" >prev</a>] [<a +href="mammult_docsu44.html#tailmammult_docsu44.html" >prev-tail</a>] [<a +href="#tailmammult_docsu45.html">tail</a>] [<a +href="mammult_docsu41.html#mammult_docsu45.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x52-510002.2.1"></a><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_linear</span><span +class="cmtt-10x-x-109">_random</span><span +class="cmtt-10x-x-109">_times</span></h5> +<!--l. 6--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 6--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_linear</span><span +class="cmbx-10x-x-109">_random</span><span +class="cmbx-10x-x-109">_times </span>- Multiplex linear preferential attachment +model – Asynchronous arrival with randomly sampled arrival times on layer +2. +<!--l. 6--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 6--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_linear</span><span +class="cmbx-10x-x-109">_random</span><span +class="cmbx-10x-x-109">_times </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m0</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">outfile</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">a</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">b</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">c</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">d</span><span +class="cmmi-10x-x-109">></span> +<!--l. 50--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 50--><p class="indent" > Grow a two-layer multiplex network using the multiplex linear preferential +attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB). +<!--l. 50--><p class="indent" > The probability for a newly arrived node <span +class="cmmi-10x-x-109">i </span>to create a link to node <span +class="cmmi-10x-x-109">j </span>on layer +1 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc21x.png" alt="Π1i→j ∝ ak[1j]+ bk[j2] +" class="math-display" ></center></td></tr></table> +<!--l. 50--><p class="nopar" > +<!--l. 50--><p class="indent" > and the dual probability for <span +class="cmmi-10x-x-109">i </span>to create a link to <span +class="cmmi-10x-x-109">j </span>on layer 2 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc22x.png" alt=" 2 [1] [2] +Π i→j ∝ ck j + dkj +" class="math-display" ></center></td></tr></table> +<!--l. 50--><p class="nopar" > +<!--l. 50--><p class="indent" > Each new node arrives on layer 1, but its replica on the other layer appears at +a uniformly chosen random time in [<span +class="cmmi-10x-x-109">m</span>0 + 1;<span +class="cmmi-10x-x-109">N</span>]. +<!--l. 50--><p class="indent" > The (mandatory) parameters are as follows: + <ul class="itemize1"> + <li class="itemize"><span +class="cmbx-10x-x-109">N </span>number of nodes in the final graph + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m </span>number of new edges brought by each new node + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span +class="cmti-10x-x-109">m0 </span>must be larger than + of equal to <span +class="cmti-10x-x-109">m</span>. + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function + </li></ul> +<!--l. 61--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 61--><p class="indent" > The program dumps on the file <span +class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the +resulting network. Each line of the file is in the format: +<!--l. 61--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 61--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 63--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 63--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 63--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> + + + + <!--l. 230--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu46.html" >next</a>] [<a +href="mammult_docsu44.html" >prev</a>] [<a +href="mammult_docsu44.html#tailmammult_docsu44.html" >prev-tail</a>] [<a +href="mammult_docsu45.html" >front</a>] [<a +href="mammult_docsu41.html#mammult_docsu45.html" >up</a>] </p></div> +<!--l. 230--><p class="indent" > <a + id="tailmammult_docsu45.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu46.html b/doc/html/mammult_docsu46.html new file mode 100644 index 0000000..e3e6edc --- /dev/null +++ b/doc/html/mammult_docsu46.html @@ -0,0 +1,40 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Non-linear preferential attachment</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 230--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu47.html" >next</a>] [<a +href="mammult_docsu45.html" >prev</a>] [<a +href="mammult_docsu45.html#tailmammult_docsu45.html" >prev-tail</a>] [<a +href="#tailmammult_docsu46.html">tail</a>] [<a +href="mammult_docse4.html#mammult_docsu46.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">2.2.2 </span> <a + id="x53-520002.2.2"></a>Non-linear preferential attachment</h4> +<!--l. 4--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu47.html#x54-530002.2.2"><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_nonlinear</span></a></span> + </div> + + + + <!--l. 235--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu47.html" >next</a>] [<a +href="mammult_docsu45.html" >prev</a>] [<a +href="mammult_docsu45.html#tailmammult_docsu45.html" >prev-tail</a>] [<a +href="mammult_docsu46.html" >front</a>] [<a +href="mammult_docse4.html#mammult_docsu46.html" >up</a>] </p></div> +<!--l. 235--><p class="indent" > <a + id="tailmammult_docsu46.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu47.html b/doc/html/mammult_docsu47.html new file mode 100644 index 0000000..d3d1192 --- /dev/null +++ b/doc/html/mammult_docsu47.html @@ -0,0 +1,142 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.2.2.0 nibilab_nonlinear</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu48.html" >next</a>] [<a +href="mammult_docsu46.html" >prev</a>] [<a +href="mammult_docsu46.html#tailmammult_docsu46.html" >prev-tail</a>] [<a +href="#tailmammult_docsu47.html">tail</a>] [<a +href="mammult_docsu46.html#mammult_docsu47.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x54-530002.2.2"></a><span +class="cmtt-10x-x-109">nibilab</span><span +class="cmtt-10x-x-109">_nonlinear</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_nonlinear </span>- Multiplex non-linear preferential attachment model – +Synchronous arrival. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">nibilab</span><span +class="cmbx-10x-x-109">_nonlinear </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">m0</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">outfile</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">alpha</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">beta</span><span +class="cmmi-10x-x-109">></span> +<!--l. 47--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 47--><p class="indent" > Grow a two-layer multiplex network using the multiplex non-linear +preferential attachment model by Nicosia, Bianconi, Latora, Barthelemy +(NiBiLaB). +<!--l. 47--><p class="indent" > The probability for a newly arrived node <span +class="cmmi-10x-x-109">i </span>to create a link to node <span +class="cmmi-10x-x-109">j </span>on layer +1 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc23x.png" alt=" ( [1])α + 1 kj +Πi→j ∝ (-[2])β- + kj +" class="math-display" ></center></td></tr></table> + + + +<!--l. 47--><p class="nopar" > +<!--l. 47--><p class="indent" > and the dual probability for <span +class="cmmi-10x-x-109">i </span>to create a link to <span +class="cmmi-10x-x-109">j </span>on layer 2 is: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc24x.png" alt=" ( )α + k[2j] +Π2i→j ∝ (---)β- + k[1j] +" class="math-display" ></center></td></tr></table> +<!--l. 47--><p class="nopar" > +<!--l. 47--><p class="indent" > Each node arrives simultaneously on both layers. +<!--l. 47--><p class="indent" > The (mandatory) parameters are as follows: + <ul class="itemize1"> + <li class="itemize"><span +class="cmbx-10x-x-109">N </span>number of nodes in the final graph + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m </span>number of new edges brought by each new node + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span +class="cmti-10x-x-109">m0 </span>must be larger than + of equal to <span +class="cmti-10x-x-109">m</span>. + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the + </li> + <li class="itemize"><span +class="cmbx-10x-x-109">alpha, beta </span>exponents of of the attaching probability function + </li></ul> +<!--l. 58--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 58--><p class="indent" > The program dumps on the file <span +class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the +resulting network. Each line of the file is in the format: +<!--l. 58--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> + + + +<!--l. 58--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 60--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 60--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 60--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> + + + + <!--l. 235--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu48.html" >next</a>] [<a +href="mammult_docsu46.html" >prev</a>] [<a +href="mammult_docsu46.html#tailmammult_docsu46.html" >prev-tail</a>] [<a +href="mammult_docsu47.html" >front</a>] [<a +href="mammult_docsu46.html#mammult_docsu47.html" >up</a>] </p></div> +<!--l. 235--><p class="indent" > <a + id="tailmammult_docsu47.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu48.html b/doc/html/mammult_docsu48.html new file mode 100644 index 0000000..d593bbd --- /dev/null +++ b/doc/html/mammult_docsu48.html @@ -0,0 +1,42 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Utilities</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 235--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu49.html" >next</a>] [<a +href="mammult_docsu47.html" >prev</a>] [<a +href="mammult_docsu47.html#tailmammult_docsu47.html" >prev-tail</a>] [<a +href="#tailmammult_docsu48.html">tail</a>] [<a +href="mammult_docse4.html#mammult_docsu48.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">2.2.3 </span> <a + id="x55-540002.2.3"></a>Utilities</h4> +<!--l. 4--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu49.html#x56-550002.2.3"><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_deg</span><span +class="cmtt-10x-x-109">_over</span><span +class="cmtt-10x-x-109">_time.py</span></a></span> + </div> + + + + <!--l. 239--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu49.html" >next</a>] [<a +href="mammult_docsu47.html" >prev</a>] [<a +href="mammult_docsu47.html#tailmammult_docsu47.html" >prev-tail</a>] [<a +href="mammult_docsu48.html" >front</a>] [<a +href="mammult_docse4.html#mammult_docsu48.html" >up</a>] </p></div> +<!--l. 239--><p class="indent" > <a + id="tailmammult_docsu48.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu49.html b/doc/html/mammult_docsu49.html new file mode 100644 index 0000000..fbe3f0c --- /dev/null +++ b/doc/html/mammult_docsu49.html @@ -0,0 +1,145 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.2.3.0 node_deg_over_time.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse5.html" >next</a>] [<a +href="mammult_docsu48.html" >prev</a>] [<a +href="mammult_docsu48.html#tailmammult_docsu48.html" >prev-tail</a>] [<a +href="#tailmammult_docsu49.html">tail</a>] [<a +href="mammult_docsu48.html#mammult_docsu49.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x56-550002.2.3"></a><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_deg</span><span +class="cmtt-10x-x-109">_over</span><span +class="cmtt-10x-x-109">_time.py</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">node</span><span +class="cmbx-10x-x-109">_deg</span><span +class="cmbx-10x-x-109">_over</span><span +class="cmbx-10x-x-109">_time.py </span>- Time evolution of the degree of a node in a +growing graph. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">node</span><span +class="cmbx-10x-x-109">_deg</span><span +class="cmbx-10x-x-109">_over</span><span +class="cmbx-10x-x-109">_time.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">arrival</span><span +class="cmitt-10x-x-109">_times</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">node</span><span +class="cmitt-10x-x-109">_id</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">node</span><span +class="cmitt-10x-x-109">_id</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 30--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 30--><p class="indent" > Compute the degree <span +class="cmmi-10x-x-109">k</span><sub><span +class="cmmi-8">i</span></sub>(<span +class="cmmi-10x-x-109">t</span>) of node <span +class="cmmi-10x-x-109">i </span>in a growing network as a function of +time. The file <span +class="cmti-10x-x-109">layer </span>contains the edge list of the final network. Each line of the +file is in the format: +<!--l. 30--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 30--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 30--><p class="indent" > The file <span +class="cmti-10x-x-109">arrival</span><span +class="cmti-10x-x-109">_times </span>is a list of node arrival times, in the format: +<!--l. 30--><p class="indent" >   <span +class="cmti-10x-x-109">time</span><span +class="cmti-10x-x-109">_i node</span><span +class="cmti-10x-x-109">_i</span> +<!--l. 30--><p class="indent" > where <span +class="cmti-10x-x-109">time</span><span +class="cmti-10x-x-109">_i </span>is the time at which <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_i </span>arrived in the graph. Notice that +<span +class="cmti-10x-x-109">time</span><span +class="cmti-10x-x-109">_i </span>must be an integer in the range [0, N-1], where N is the total number of +nodes in the final graph. +<!--l. 30--><p class="indent" > The third parameter <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_id </span>is the ID of the node whose degree over time +will be printed on output. If more than one <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_id </span>is provided, the degrees over +time of all the corresponding nodes are printed on output. +<!--l. 48--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 48--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines in the format: + + + +<!--l. 48--><p class="indent" >   <span +class="cmti-10x-x-109">t kit</span> +<!--l. 48--><p class="indent" > where <span +class="cmti-10x-x-109">kit </span>is the degree of node <span +class="cmti-10x-x-109">i </span>at time <span +class="cmti-10x-x-109">t</span>. The first line of output is in the +format: +<!--l. 48--><p class="indent" >   <span +class="cmti-10x-x-109">#### node</span><span +class="cmti-10x-x-109">_id</span> +<!--l. 48--><p class="indent" > where <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_id </span>is the ID of node <span +class="cmti-10x-x-109">i</span>. +<!--l. 48--><p class="indent" > If more than one <span +class="cmti-10x-x-109">node</span><span +class="cmti-10x-x-109">_id</span>s is provided as input, the program prints the degree +over time of all of them, sequentially. +<!--l. 50--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 50--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 50--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> + + + + <!--l. 239--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse5.html" >next</a>] [<a +href="mammult_docsu48.html" >prev</a>] [<a +href="mammult_docsu48.html#tailmammult_docsu48.html" >prev-tail</a>] [<a +href="mammult_docsu49.html" >front</a>] [<a +href="mammult_docsu48.html#mammult_docsu49.html" >up</a>] </p></div> +<!--l. 239--><p class="indent" > <a + id="tailmammult_docsu49.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu5.html b/doc/html/mammult_docsu5.html new file mode 100644 index 0000000..88c4386 --- /dev/null +++ b/doc/html/mammult_docsu5.html @@ -0,0 +1,95 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 layer_activity_vectors.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu6.html" >next</a>] [<a +href="mammult_docsu4.html" >prev</a>] [<a +href="mammult_docsu4.html#tailmammult_docsu4.html" >prev-tail</a>] [<a +href="#tailmammult_docsu5.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu5.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x8-70001.1.1"></a><span +class="cmtt-10x-x-109">layer</span><span +class="cmtt-10x-x-109">_activity</span><span +class="cmtt-10x-x-109">_vectors.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">layer</span><span +class="cmbx-10x-x-109">_activity</span><span +class="cmbx-10x-x-109">_vectors.py </span>- compute the activity vectors of all the layers of +a multiplex. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">layer</span><span +class="cmbx-10x-x-109">_activity</span><span +class="cmbx-10x-x-109">_vectors.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 15--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 15--><p class="indent" > Compute and print on output the activity vectors of the layers of a multiplex +network, where the layers are given as input in the files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, +etc. +<!--l. 15--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 15--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 15--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 25--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 25--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains the +activity vector of the n-th layer, i.e. a bit-string where each bit is set to +“1” if the corresponding node is active on the n-th layer, and to “0” +otherwise. +<!--l. 25--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if +a node ID is not present in any of the layer files given as input, the program +considers it as being isolated on all the layers. +<!--l. 27--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 27--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 27--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu6.html" >next</a>] [<a +href="mammult_docsu4.html" >prev</a>] [<a +href="mammult_docsu4.html#tailmammult_docsu4.html" >prev-tail</a>] [<a +href="mammult_docsu5.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu5.html" >up</a>] </p></div> +<!--l. 4--><p class="indent" > <a + id="tailmammult_docsu5.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu50.html b/doc/html/mammult_docsu50.html new file mode 100644 index 0000000..693e7d9 --- /dev/null +++ b/doc/html/mammult_docsu50.html @@ -0,0 +1,46 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Models based on simulated annealing</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 241--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu51.html" >next</a>] [<a +href="mammult_docse5.html" >prev</a>] [<a +href="mammult_docse5.html#tailmammult_docse5.html" >prev-tail</a>] [<a +href="#tailmammult_docsu50.html">tail</a>] [<a +href="mammult_docse5.html#mammult_docsu50.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">2.3.1 </span> <a + id="x58-570002.3.1"></a>Models based on simulated annealing</h4> +<!--l. 3--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu51.html#x59-580002.3.1"><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_rho</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu52.html#x60-590002.3.1"><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_qnn</span><span +class="cmtt-10x-x-109">_adaptive</span></a></span> + </div> + + + + + <!--l. 247--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu51.html" >next</a>] [<a +href="mammult_docse5.html" >prev</a>] [<a +href="mammult_docse5.html#tailmammult_docse5.html" >prev-tail</a>] [<a +href="mammult_docsu50.html" >front</a>] [<a +href="mammult_docse5.html#mammult_docsu50.html" >up</a>] </p></div> +<!--l. 247--><p class="indent" > <a + id="tailmammult_docsu50.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu51.html b/doc/html/mammult_docsu51.html new file mode 100644 index 0000000..8eab351 --- /dev/null +++ b/doc/html/mammult_docsu51.html @@ -0,0 +1,113 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.3.1.0 tune_rho</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu52.html" >next</a>] [<a +href="mammult_docsu50.html" >prev</a>] [<a +href="mammult_docsu50.html#tailmammult_docsu50.html" >prev-tail</a>] [<a +href="#tailmammult_docsu51.html">tail</a>] [<a +href="mammult_docsu50.html#mammult_docsu51.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x59-580002.3.1"></a><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_rho</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">tune</span><span +class="cmbx-10x-x-109">_rho </span>- Construct a multiplex with prescribed inter-layer correlations. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">tune</span><span +class="cmbx-10x-x-109">_rho </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">rank1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">rank2</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">rho</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">eps</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">beta</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[RND|NAT|INV]</span> +<!--l. 33--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 33--><p class="indent" > This programs tunes the inter-layer degree correlation coefficient <span +class="cmmi-10x-x-109">ρ</span> +(Spearman’s rank correlation) of two layers, by adjusting the inter-layer pairing +of nodes. The files <span +class="cmti-10x-x-109">rank1 </span>and <span +class="cmti-10x-x-109">rank2 </span>are the rankings of nodes in the first and +second layer, where the n-th line of the file contains the rank of the n-th node +(the highest ranked node has rank equal to 1). + + + +<!--l. 33--><p class="indent" > The parameter <span +class="cmti-10x-x-109">rho </span>is the desired value of the Spearman’s rank correlation +coefficient, while <span +class="cmti-10x-x-109">eps </span>is the accuracy of <span +class="cmti-10x-x-109">rho</span>. For instance, if <span +class="cmti-10x-x-109">rho </span>is set equal to +-0.25 and <span +class="cmti-10x-x-109">eps </span>is equal to 0.0001, the program stops when the configuration of +node pairing corresponds to a value of <span +class="cmmi-10x-x-109">ρ </span>which differs from -0.25 by less than +0.0001. +<!--l. 33--><p class="indent" > The parameter <span +class="cmti-10x-x-109">beta </span>is the typical inverse temperature of simulated +annealing. +<!--l. 33--><p class="indent" > If no other parameter is specified, or if the last parameter is <span +class="cmtt-10x-x-109">RND</span>, the program +starts from a random pairing of nodes. If the last parameter is <span +class="cmtt-10x-x-109">NAT </span>then the +program assumes that the initial pairing is the natural one, where the nodes have +the same ID on both layers. Finally, if <span +class="cmtt-10x-x-109">INV </span>is specified, the initial pairing is the +inverse pairing, i.e. the one where node 0 on layer 1 is paired with node N-1 on +layer 2, and so on. +<!--l. 43--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 43--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a pairing, i.e. a list of lines in the +format: +<!--l. 43--><p class="indent" >   <span +class="cmti-10x-x-109">IDL1 IDL2</span> +<!--l. 43--><p class="indent" > where <span +class="cmti-10x-x-109">IDL1 </span>is the ID of the node on layer 1 and <span +class="cmti-10x-x-109">IDL2 </span>is the corresponding +ID of the same node on layer 2. +<!--l. 45--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 45--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 45--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu52.html" >next</a>] [<a +href="mammult_docsu50.html" >prev</a>] [<a +href="mammult_docsu50.html#tailmammult_docsu50.html" >prev-tail</a>] [<a +href="mammult_docsu51.html" >front</a>] [<a +href="mammult_docsu50.html#mammult_docsu51.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu51.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu52.html b/doc/html/mammult_docsu52.html new file mode 100644 index 0000000..b0e0444 --- /dev/null +++ b/doc/html/mammult_docsu52.html @@ -0,0 +1,148 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>2.3.1.0 tune_qnn_adaptive</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docch3.html" >next</a>] [<a +href="mammult_docsu51.html" >prev</a>] [<a +href="mammult_docsu51.html#tailmammult_docsu51.html" >prev-tail</a>] [<a +href="#tailmammult_docsu52.html">tail</a>] [<a +href="mammult_docsu50.html#mammult_docsu52.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x60-590002.3.1"></a><span +class="cmtt-10x-x-109">tune</span><span +class="cmtt-10x-x-109">_qnn</span><span +class="cmtt-10x-x-109">_adaptive</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">tune</span><span +class="cmbx-10x-x-109">_qnn</span><span +class="cmbx-10x-x-109">_adaptive </span>- Construct a multiplex with prescribed inter-layer +correlations. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">tune</span><span +class="cmbx-10x-x-109">_qnn</span><span +class="cmbx-10x-x-109">_adaptive </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">degs1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">degs2</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">mu</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">eps</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">beta</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmitt-10x-x-109">[RND|NAT|INV]</span> +<!--l. 52--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 52--><p class="indent" > This programs tunes the inter-layer degree correlation exponent <span +class="cmmi-10x-x-109">μ</span>. If +we consider two layers of a multiplex, and we denote by <span +class="cmmi-10x-x-109">k </span>the degree +of a node on the first layer and by <span +class="cmmi-10x-x-109">q </span>the degree of the same node on +the second layers, the inter-layer degree correlation function is defined +as: + <table +class="equation-star"><tr><td> + <center class="math-display" > +<img +src="mammult_doc25x.png" alt="-- ∑ ′ ′ +q(k) = q P(q |k) + q′ +" class="math-display" ></center></td></tr></table> +<!--l. 52--><p class="nopar" > +<!--l. 52--><p class="indent" > where <span class="overline"><span +class="cmmi-10x-x-109">q</span></span>(<span +class="cmmi-10x-x-109">k</span>) is the average degree on layer 2 of nodes having degree <span +class="cmmi-10x-x-109">k </span>on layer +1. +<!--l. 52--><p class="indent" > The program assumes that we want to set the degree correlation function +such that: + <table +class="equation-star"><tr><td> + + + + <center class="math-display" > +<img +src="mammult_doc26x.png" alt="q(k) = akμ +" class="math-display" ></center></td></tr></table> +<!--l. 52--><p class="nopar" > +<!--l. 52--><p class="indent" > where the exponent of the power-law function is given by the user +(it is indeed the parameter <span +class="cmti-10x-x-109">mu</span>), and successively adjusts the pairing +between nodes at the two layers in order to obtain a correlation function as +close as possible to the desired one. The files <span +class="cmti-10x-x-109">degs1 </span>and <span +class="cmti-10x-x-109">degs2 </span>contain, +respectively, the degrees of the nodes on the first layer and on the second +layer. +<!--l. 52--><p class="indent" > The parameter <span +class="cmti-10x-x-109">eps </span>is the accuracy of <span +class="cmti-10x-x-109">mu</span>. For instance, if <span +class="cmti-10x-x-109">mu </span>is set equal to +-0.25 and <span +class="cmti-10x-x-109">eps </span>is equal to 0.0001, the program stops when the configuration of +node pairing corresponds to a value of the exponent <span +class="cmmi-10x-x-109">μ </span>which differs from -0.25 by +less than 0.0001. +<!--l. 52--><p class="indent" > The parameter <span +class="cmti-10x-x-109">beta </span>is the typical inverse temperature of simulated +annealing. +<!--l. 52--><p class="indent" > If no other parameter is specified, or if the last parameter is <span +class="cmtt-10x-x-109">RND</span>, the program +starts from a random pairing of nodes. If the last parameter is <span +class="cmtt-10x-x-109">NAT </span>then the +program assumes that the initial pairing is the natural one, where the nodes have +the same ID on both layers. Finally, if <span +class="cmtt-10x-x-109">INV </span>is specified, the initial pairing is the +inverse pairing, i.e. the one where node 0 on layer 1 is paired with node N-1 on +layer 2, and so on. +<!--l. 62--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 62--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a pairing, i.e. a list of lines in the +format: +<!--l. 62--><p class="indent" >   <span +class="cmti-10x-x-109">IDL1 IDL2</span> +<!--l. 62--><p class="indent" > where <span +class="cmti-10x-x-109">IDL1 </span>is the ID of the node on layer 1 and <span +class="cmti-10x-x-109">IDL2 </span>is the corresponding +ID of the same node on layer 2. +<!--l. 64--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 64--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 64--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 247--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docch3.html" >next</a>] [<a +href="mammult_docsu51.html" >prev</a>] [<a +href="mammult_docsu51.html#tailmammult_docsu51.html" >prev-tail</a>] [<a +href="mammult_docsu52.html" >front</a>] [<a +href="mammult_docsu50.html#mammult_docsu52.html" >up</a>] </p></div> +<!--l. 247--><p class="indent" > <a + id="tailmammult_docsu52.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu53.html b/doc/html/mammult_docsu53.html new file mode 100644 index 0000000..bf48733 --- /dev/null +++ b/doc/html/mammult_docsu53.html @@ -0,0 +1,123 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>3.1.0.0 multiplex_ising</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse7.html" >next</a>] [<a +href="mammult_docse6.html" >prev</a>] [<a +href="mammult_docse6.html#tailmammult_docse6.html" >prev-tail</a>] [<a +href="#tailmammult_docsu53.html">tail</a>] [<a +href="mammult_docse6.html#mammult_docsu53.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x63-620003.1"></a><span +class="cmtt-10x-x-109">multiplex</span><span +class="cmtt-10x-x-109">_ising</span></h5> +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">multiplex</span><span +class="cmbx-10x-x-109">_ising </span>- compute the coupled ising model in a multiplex with 2 +layers. +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">multiplex</span><span +class="cmbx-10x-x-109">_ising </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">T</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">J</span><span +class="cmmi-10x-x-109">> < γ > < h</span><sup><span +class="cmr-8">[1]</span></sup> <span +class="cmmi-10x-x-109">></span> +<span +class="cmmi-10x-x-109">< h</span><sup><span +class="cmr-8">[2]</span></sup> <span +class="cmmi-10x-x-109">> < p</span><sub><span +class="cmr-8">1</span></sub> <span +class="cmmi-10x-x-109">> < p</span><sub><span +class="cmr-8">2</span></sub> <span +class="cmmi-10x-x-109">> < numepochs ></span> +<!--l. 18--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 18--><p class="indent" > Compute and print the output of the ising dynamics on two coupled layers of +a multiplex network. Files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, contain the (undirected) edge list of the +two layer, and each line is in the format: +<!--l. 18--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 18--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 18--><p class="indent" > <span +class="cmmi-10x-x-109">T </span>is the value of thermal noise in the system, <span +class="cmmi-10x-x-109">J </span>the value of peer pressure, <span +class="cmmi-10x-x-109">γ</span> +the relative ratio between internal coupling and peer pressure, <span +class="cmmi-10x-x-109">h</span><sup><span +class="cmr-8">[1]</span></sup> and <span +class="cmmi-10x-x-109">h</span><sup><span +class="cmr-8">[2]</span></sup> the +external fields acting on the two layers, <span +class="cmmi-10x-x-109">p</span><sub><span +class="cmr-8">1</span></sub> the probability for a spin on layer 1 at +<span +class="cmmi-10x-x-109">t </span>= 0 to be up, <span +class="cmmi-10x-x-109">p</span><sub><span +class="cmr-8">2</span></sub> the same probability for spins on layer 2, <span +class="cmmi-10x-x-109">numepochs </span>the + + + +number of epochs for the simulation. +<!--l. 20--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 20--><p class="indent" > One line, reporting all controlling parameter, the value of consensus in +layer 1 <span +class="cmmi-10x-x-109">m</span><sup><span +class="cmr-8">[1]</span></sup>, the value of consensus in layer 2 <span +class="cmmi-10x-x-109">m</span><sup><span +class="cmr-8">[2]</span></sup> and the coherence +<span +class="cmmi-10x-x-109">C</span>. +<!--l. 22--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 22--><p class="indent" > F. Battiston, A. Cairoli, V. Nicosia, A. Baule, V. Latora, <span +class="cmti-10x-x-109">“Interplay between</span> +<span +class="cmti-10x-x-109">consensus and coherence in a model of interacting opinions”</span>, accepted for +publication in Physica D, arxiv:1506.04544 (2015). +<!--l. 22--><p class="indent" > Link to paper: <a +href="http://arxiv.org/abs/1506.04544" class="url" ><span +class="cmtt-10x-x-109">http://arxiv.org/abs/1506.04544</span></a> + + + + <!--l. 253--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docse7.html" >next</a>] [<a +href="mammult_docse6.html" >prev</a>] [<a +href="mammult_docse6.html#tailmammult_docse6.html" >prev-tail</a>] [<a +href="mammult_docsu53.html" >front</a>] [<a +href="mammult_docse6.html#mammult_docsu53.html" >up</a>] </p></div> +<!--l. 253--><p class="indent" > <a + id="tailmammult_docsu53.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu54.html b/doc/html/mammult_docsu54.html new file mode 100644 index 0000000..ecdc0ad --- /dev/null +++ b/doc/html/mammult_docsu54.html @@ -0,0 +1,39 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Stationary distribution</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 255--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu55.html" >next</a>] [<a +href="mammult_docse7.html" >prev</a>] [<a +href="mammult_docse7.html#tailmammult_docse7.html" >prev-tail</a>] [<a +href="#tailmammult_docsu54.html">tail</a>] [<a +href="mammult_docse7.html#mammult_docsu54.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">3.2.1 </span> <a + id="x65-640003.2.1"></a>Stationary distribution</h4> +<!--l. 7--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu55.html#x66-650003.2.1"><span +class="cmtt-10x-x-109">statdistr2</span></a></span> + </div> + + + + <!--l. 259--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu55.html" >next</a>] [<a +href="mammult_docse7.html" >prev</a>] [<a +href="mammult_docse7.html#tailmammult_docse7.html" >prev-tail</a>] [<a +href="mammult_docsu54.html" >front</a>] [<a +href="mammult_docse7.html#mammult_docsu54.html" >up</a>] </p></div> +<!--l. 259--><p class="indent" > <a + id="tailmammult_docsu54.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu55.html b/doc/html/mammult_docsu55.html new file mode 100644 index 0000000..dbe980d --- /dev/null +++ b/doc/html/mammult_docsu55.html @@ -0,0 +1,121 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>3.2.1.0 statdistr2</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu56.html" >next</a>] [<a +href="mammult_docsu54.html" >prev</a>] [<a +href="mammult_docsu54.html#tailmammult_docsu54.html" >prev-tail</a>] [<a +href="#tailmammult_docsu55.html">tail</a>] [<a +href="mammult_docsu54.html#mammult_docsu55.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x66-650003.2.1"></a><span +class="cmtt-10x-x-109">statdistr2</span></h5> +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">statdistr2 </span>- compute the stationary distribution of additive, multiplicative +and intensive biased walks in a multiplex with 2 layers. +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">statdistr2 </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> < overlappingnetwork > <</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">> b</span><sub><span +class="cmr-8">1</span></sub> +<span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> +<!--l. 20--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> + + + +<!--l. 20--><p class="indent" > Compute and print the stationary distribution of additive, multiplicative and +intensive biased walks in a multiplex with 2 layers. Files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, +contain the (undirected) edge list of the two layer, and each line is in the +format: +<!--l. 20--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 20--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 20--><p class="indent" > The file <span +class="cmti-10x-x-109">overlapping network </span>has also a third column indicating the number of +times two nodes are connected across all layers. +<!--l. 20--><p class="indent" > <span +class="cmmi-10x-x-109">N </span>is the number of nodes, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> is the first bias exponent (the bias exponent +for layer 1 for additive and multiplicative walks, the bias exponent on +the participation coefficient for intensive walks), <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> is the second bias +exponent (the bias exponent for layer 1 for additive and multiplicative +walks, the bias exponent on the participation coefficient for intensive +walks). +<!--l. 22--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 22--><p class="indent" > N lines. In the n-th line we report the node ID, the stationary distribution of +that node for additive walks with exponents <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub>, the stationary distribution +for multiplicative walks with exponents <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub>, the stationary distribution for +multiplicative walks with exponents <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub>, the values of the bias exponents <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> +and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub>. +<!--l. 24--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 24--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, <span +class="cmti-10x-x-109">“Biased random walks on multiplex</span> +<span +class="cmti-10x-x-109">networks”</span>, arxiv:1505.01378 (2015). +<!--l. 24--><p class="indent" > Link to paper: <a +href="http://arxiv.org/abs/1505.01378" class="url" ><span +class="cmtt-10x-x-109">http://arxiv.org/abs/1505.01378</span></a> + + + + <!--l. 259--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu56.html" >next</a>] [<a +href="mammult_docsu54.html" >prev</a>] [<a +href="mammult_docsu54.html#tailmammult_docsu54.html" >prev-tail</a>] [<a +href="mammult_docsu55.html" >front</a>] [<a +href="mammult_docsu54.html#mammult_docsu55.html" >up</a>] </p></div> +<!--l. 259--><p class="indent" > <a + id="tailmammult_docsu55.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu56.html b/doc/html/mammult_docsu56.html new file mode 100644 index 0000000..b3ace9c --- /dev/null +++ b/doc/html/mammult_docsu56.html @@ -0,0 +1,43 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>Entropy rate</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 259--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu57.html" >next</a>] [<a +href="mammult_docsu55.html" >prev</a>] [<a +href="mammult_docsu55.html#tailmammult_docsu55.html" >prev-tail</a>] [<a +href="#tailmammult_docsu56.html">tail</a>] [<a +href="mammult_docse7.html#mammult_docsu56.html" >up</a>] </p></div> + <h4 class="subsectionHead"><span class="titlemark">3.2.2 </span> <a + id="x67-660003.2.2"></a>Entropy rate</h4> +<!--l. 7--><p class="noindent" > + <div class="subsubsectionTOCS"> +    <span class="subsubsectionToc" ><a +href="mammult_docsu57.html#x68-670003.2.2"><span +class="cmtt-10x-x-109">entropyrate2add</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu58.html#x69-680003.2.2"><span +class="cmtt-10x-x-109">entropyrate2mult</span></a></span> +<br />    <span class="subsubsectionToc" ><a +href="mammult_docsu59.html#x70-690003.2.2"><span +class="cmtt-10x-x-109">entropyrate2int</span></a></span> + </div> + +<!--l. 265--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu57.html" >next</a>] [<a +href="mammult_docsu55.html" >prev</a>] [<a +href="mammult_docsu55.html#tailmammult_docsu55.html" >prev-tail</a>] [<a +href="mammult_docsu56.html" >front</a>] [<a +href="mammult_docse7.html#mammult_docsu56.html" >up</a>] </p></div> +<!--l. 265--><p class="indent" > <a + id="tailmammult_docsu56.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu57.html b/doc/html/mammult_docsu57.html new file mode 100644 index 0000000..d236995 --- /dev/null +++ b/doc/html/mammult_docsu57.html @@ -0,0 +1,112 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>3.2.2.0 entropyrate2add</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu58.html" >next</a>] [<a +href="mammult_docsu56.html" >prev</a>] [<a +href="mammult_docsu56.html#tailmammult_docsu56.html" >prev-tail</a>] [<a +href="#tailmammult_docsu57.html">tail</a>] [<a +href="mammult_docsu56.html#mammult_docsu57.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x68-670003.2.2"></a><span +class="cmtt-10x-x-109">entropyrate2add</span></h5> +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">entropyrate2add </span>- compute the entropy rate of additive biased walks in a +multiplex with 2 layers. +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">entropyrate2add </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> < overlappingnetwork > <</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> +<!--l. 20--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 20--><p class="indent" > Compute and print the entropy rate of an additive biased walk in a +multiplex with 2 layers and bias parameters <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub>. Files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, +contain the (undirected) edge list of the two layer, and each line is in the +format: +<!--l. 20--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 20--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 20--><p class="indent" > The file <span +class="cmti-10x-x-109">overlapping network </span>has also a third column indicating the number of +times two nodes are connected across all layers. +<!--l. 20--><p class="indent" > <span +class="cmmi-10x-x-109">N </span>is the number of nodes, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> is the degree-biased exponent for layer 1, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> is +the degree-biased exponent for layer 2. +<!--l. 22--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 22--><p class="indent" > One line, reporting the value of the entropy rate <span +class="cmmi-10x-x-109">h </span>of an additive biased +random walks with <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> as bias exponents, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub>. + + + +<!--l. 24--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 24--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, <span +class="cmti-10x-x-109">“Biased random walks on multiplex</span> +<span +class="cmti-10x-x-109">networks”</span>, arxiv:1505.01378 (2015). +<!--l. 24--><p class="indent" > Link to paper: <a +href="http://arxiv.org/abs/1505.01378" class="url" ><span +class="cmtt-10x-x-109">http://arxiv.org/abs/1505.01378</span></a> + + + + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu58.html" >next</a>] [<a +href="mammult_docsu56.html" >prev</a>] [<a +href="mammult_docsu56.html#tailmammult_docsu56.html" >prev-tail</a>] [<a +href="mammult_docsu57.html" >front</a>] [<a +href="mammult_docsu56.html#mammult_docsu57.html" >up</a>] </p></div> +<!--l. 7--><p class="indent" > <a + id="tailmammult_docsu57.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu58.html b/doc/html/mammult_docsu58.html new file mode 100644 index 0000000..6aeaf8c --- /dev/null +++ b/doc/html/mammult_docsu58.html @@ -0,0 +1,109 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>3.2.2.0 entropyrate2mult</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu59.html" >next</a>] [<a +href="mammult_docsu57.html" >prev</a>] [<a +href="mammult_docsu57.html#tailmammult_docsu57.html" >prev-tail</a>] [<a +href="#tailmammult_docsu58.html">tail</a>] [<a +href="mammult_docsu56.html#mammult_docsu58.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x69-680003.2.2"></a><span +class="cmtt-10x-x-109">entropyrate2mult</span></h5> +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">entropyrate2mult </span>- compute the entropy rate of multiplicative biased walks +in a multiplex with 2 layers. +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">entropyrate2mult </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> < overlappingnetwork > <</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">></span> +<span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> +<!--l. 20--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 20--><p class="indent" > Compute and print the entropy rate of a multiplicative biased walk in a +multiplex with 2 layers and bias parameters <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub>. Files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, +contain the (undirected) edge list of the two layer, and each line is in the +format: +<!--l. 20--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 20--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 20--><p class="indent" > The file <span +class="cmti-10x-x-109">overlapping network </span>has also a third column indicating the number of +times two nodes are connected across all layers. +<!--l. 20--><p class="indent" > <span +class="cmmi-10x-x-109">N </span>is the number of nodes, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> is the degree-biased exponent for layer 1, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> is +the degree-biased exponent for layer 2. +<!--l. 22--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 22--><p class="indent" > One line, reporting the value of the entropy rate <span +class="cmmi-10x-x-109">h </span>of an multiplicative biased +random walks with <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> as bias exponents, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">1</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub>. +<!--l. 24--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 24--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, <span +class="cmti-10x-x-109">“Biased random walks on multiplex</span> +<span +class="cmti-10x-x-109">networks”</span>, arxiv:1505.01378 (2015). +<!--l. 24--><p class="indent" > Link to paper: <a +href="http://arxiv.org/abs/1505.01378" class="url" ><span +class="cmtt-10x-x-109">http://arxiv.org/abs/1505.01378</span></a> + + + + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu59.html" >next</a>] [<a +href="mammult_docsu57.html" >prev</a>] [<a +href="mammult_docsu57.html#tailmammult_docsu57.html" >prev-tail</a>] [<a +href="mammult_docsu58.html" >front</a>] [<a +href="mammult_docsu56.html#mammult_docsu58.html" >up</a>] </p></div> +<!--l. 7--><p class="indent" > <a + id="tailmammult_docsu58.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu59.html b/doc/html/mammult_docsu59.html new file mode 100644 index 0000000..7baf3e6 --- /dev/null +++ b/doc/html/mammult_docsu59.html @@ -0,0 +1,103 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>3.2.2.0 entropyrate2int</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 7--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu58.html" >prev</a>] [<a +href="mammult_docsu58.html#tailmammult_docsu58.html" >prev-tail</a>] [<a +href="#tailmammult_docsu59.html">tail</a>] [<a +href="mammult_docsu56.html#mammult_docsu59.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x70-690003.2.2"></a><span +class="cmtt-10x-x-109">entropyrate2int</span></h5> +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">entropyrate2int </span>- compute the entropy rate of intensive biased walks in a +multiplex with 2 layers. +<!--l. 7--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 7--><p class="indent" > <span +class="cmbx-10x-x-109">entropyrate2int </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> < overlappingnetwork > <</span><span +class="cmitt-10x-x-109">N</span><span +class="cmmi-10x-x-109">> b</span><sub><span +class="cmr-8">1</span></sub> +<span +class="cmmi-10x-x-109">b</span><sub><span +class="cmr-8">2</span></sub> +<!--l. 20--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 20--><p class="indent" > Compute and print the entropy rate of an intensive biased walks in a +multiplex with 2 layers and bias parameters <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmmi-8">p</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmmi-8">o</span></sub>. Files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, +contain the (undirected) edge list of the two layer, and each line is in the +format: +<!--l. 20--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 20--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 20--><p class="indent" > The file <span +class="cmti-10x-x-109">overlapping network </span>has also a third column indicating the number of +times two nodes are connected across all layers. +<!--l. 20--><p class="indent" > <span +class="cmmi-10x-x-109">N </span>is the number of nodes, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmmi-8">p</span></sub> is the biased exponent on the participation +coefficient, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmmi-8">o</span></sub> is the biased exponent on the overlapping degree. +<!--l. 22--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 22--><p class="indent" > One line, reporting the value of the entropy rate <span +class="cmmi-10x-x-109">h </span>of an intensive biased +random walks with <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmmi-8">p</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmmi-8">o</span></sub> as bias exponents, <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmmi-8">p</span></sub> and <span +class="cmmi-10x-x-109">b</span><sub><span +class="cmmi-8">o</span></sub>. +<!--l. 24--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 24--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, <span +class="cmti-10x-x-109">“Biased random walks on multiplex</span> +<span +class="cmti-10x-x-109">networks”</span>, arxiv:1505.01378 (2015). +<!--l. 24--><p class="indent" > Link to paper: <a +href="http://arxiv.org/abs/1505.01378" class="url" ><span +class="cmtt-10x-x-109">http://arxiv.org/abs/1505.01378</span></a> + <!--l. 265--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu58.html" >prev</a>] [<a +href="mammult_docsu58.html#tailmammult_docsu58.html" >prev-tail</a>] [<a +href="mammult_docsu59.html" >front</a>] [<a +href="mammult_docsu56.html#mammult_docsu59.html" >up</a>] </p></div> +<!--l. 265--><p class="indent" > <a + id="tailmammult_docsu59.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu6.html b/doc/html/mammult_docsu6.html new file mode 100644 index 0000000..1c83cb0 --- /dev/null +++ b/doc/html/mammult_docsu6.html @@ -0,0 +1,101 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 multiplexity.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu7.html" >next</a>] [<a +href="mammult_docsu5.html" >prev</a>] [<a +href="mammult_docsu5.html#tailmammult_docsu5.html" >prev-tail</a>] [<a +href="#tailmammult_docsu6.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu6.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x9-80001.1.1"></a><span +class="cmtt-10x-x-109">multiplexity.py</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">multiplexity.py </span>- compute the pairwise multiplexity between all the pairs of +layers of a multiplex. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">multiplexity.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer3</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 17--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 17--><p class="indent" > Compute and print on output the pairwise multiplexity <span +class="cmmi-10x-x-109">Q</span><sub><span +class="cmmi-8">α,β</span></sub> (i.e., the +fraction of nodes active on both layers) between all pairs of layers. The layers are +given as input in the files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, etc. +<!--l. 17--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 17--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 17--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 28--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 28--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines, in the format: +<!--l. 28--><p class="indent" >   <span +class="cmti-10x-x-109">layer1 layer2 mult</span> +<!--l. 28--><p class="noindent" >where <span +class="cmti-10x-x-109">layer1 </span>and <span +class="cmti-10x-x-109">layer2 </span>are the IDs of the layers, and <span +class="cmti-10x-x-109">mult </span>is the value of the +multiplexity <span +class="cmmi-10x-x-109">Q</span><sub><span +class="cmmi-8">layer</span><span +class="cmr-8">1</span><span +class="cmmi-8">,layer</span><span +class="cmr-8">2</span></sub>. Layers IDs start from zero, are are associated to the +layers in the same order in which the layer files are provided on the command +line. +<!--l. 30--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 30--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 30--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu7.html" >next</a>] [<a +href="mammult_docsu5.html" >prev</a>] [<a +href="mammult_docsu5.html#tailmammult_docsu5.html" >prev-tail</a>] [<a +href="mammult_docsu6.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu6.html" >up</a>] </p></div> +<!--l. 4--><p class="indent" > <a + id="tailmammult_docsu6.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu7.html b/doc/html/mammult_docsu7.html new file mode 100644 index 0000000..6d0949e --- /dev/null +++ b/doc/html/mammult_docsu7.html @@ -0,0 +1,105 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 hamming_dist.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu8.html" >next</a>] [<a +href="mammult_docsu6.html" >prev</a>] [<a +href="mammult_docsu6.html#tailmammult_docsu6.html" >prev-tail</a>] [<a +href="#tailmammult_docsu7.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu7.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x10-90001.1.1"></a><span +class="cmtt-10x-x-109">hamming</span><span +class="cmtt-10x-x-109">_dist.py</span></h5> +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">hamming</span><span +class="cmbx-10x-x-109">_dist.py </span>- compute the normalised Hamming distance between all +the pairs of layers of a multiplex. +<!--l. 4--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 4--><p class="indent" > <span +class="cmbx-10x-x-109">hamming</span><span +class="cmbx-10x-x-109">_dist.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> <</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer3</span><span +class="cmmi-10x-x-109">></span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 18--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 18--><p class="indent" > Compute and print on output the normalised Hamming distance <span +class="cmmi-10x-x-109">H</span><sub><span +class="cmmi-8">α,β</span></sub> (i.e., +the fraction of nodes which are active on either of the layers, but not on both) +between all pairs of layers. The layers are given as input in the files <span +class="cmti-10x-x-109">layer1</span>, +<span +class="cmti-10x-x-109">layer2</span>, etc. +<!--l. 18--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is +in the format: +<!--l. 18--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 18--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 29--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 29--><p class="indent" > The program prints on <span +class="cmtt-10x-x-109">stdout </span>a list of lines, in the format: +<!--l. 29--><p class="indent" >   <span +class="cmti-10x-x-109">layer1 layer2 hamm</span> +<!--l. 29--><p class="noindent" >where <span +class="cmti-10x-x-109">layer1 </span>and <span +class="cmti-10x-x-109">layer2 </span>are the IDs of the layers, and <span +class="cmti-10x-x-109">hamm </span>is the value of the +normalised Haming distance <span +class="cmmi-10x-x-109">H</span><sub><span +class="cmmi-8">layer</span><span +class="cmr-8">1</span><span +class="cmmi-8">,layer</span><span +class="cmr-8">2</span></sub>. Layers IDs start from zero, are are +associated to the layers in the same order in which the layer files are provided on +the command line. +<!--l. 31--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 31--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 31--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu8.html" >next</a>] [<a +href="mammult_docsu6.html" >prev</a>] [<a +href="mammult_docsu6.html#tailmammult_docsu6.html" >prev-tail</a>] [<a +href="mammult_docsu7.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu7.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu7.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu8.html b/doc/html/mammult_docsu8.html new file mode 100644 index 0000000..2bbfd90 --- /dev/null +++ b/doc/html/mammult_docsu8.html @@ -0,0 +1,109 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 node_degree_vectors.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu9.html" >next</a>] [<a +href="mammult_docsu7.html" >prev</a>] [<a +href="mammult_docsu7.html#tailmammult_docsu7.html" >prev-tail</a>] [<a +href="#tailmammult_docsu8.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu8.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x11-100001.1.1"></a><span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_degree</span><span +class="cmtt-10x-x-109">_vectors.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">node</span><span +class="cmbx-10x-x-109">_degree</span><span +class="cmbx-10x-x-109">_vectors.py </span>- compute the degree vectors of all the nodes of a +multiplex network +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">node</span><span +class="cmbx-10x-x-109">_degree</span><span +class="cmbx-10x-x-109">_vectors.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer1</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">[</span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">layer2</span><span +class="cmmi-10x-x-109">> </span><span +class="cmitt-10x-x-109">...]</span> +<!--l. 15--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 15--><p class="indent" > Compute and print on output the degree vectors of all the nodes of a +multiplex network, whose layers are given as input in the files <span +class="cmti-10x-x-109">layer1</span>, <span +class="cmti-10x-x-109">layer2</span>, +etc. +<!--l. 15--><p class="indent" > Each file contains the (undirected) edge list of a layer, and each line is in the +format: +<!--l. 15--><p class="indent" >   <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID dest</span><span +class="cmti-10x-x-109">_ID</span> +<!--l. 15--><p class="indent" > where <span +class="cmti-10x-x-109">src</span><span +class="cmti-10x-x-109">_ID </span>and <span +class="cmti-10x-x-109">dest</span><span +class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an +edge. +<!--l. 27--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 27--><p class="indent" > A list of lines, where the n-th line is the vector of degrees of the n-th node, in +the format: +<!--l. 27--><p class="indent" >   <span +class="cmti-10x-x-109">noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_lay1 noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_lay2 ... noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_layM</span> +<!--l. 27--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if +a node ID is not present in any of the layer files given as input, the program +considers it as being isolated on all the layers. +<!--l. 29--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 29--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. Lett. </span><span +class="cmbx-10x-x-109">111</span>, 058701 (2013). +<!--l. 29--><p class="indent" > Link to paper: <a +href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span +class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a> +<br +class="newline" /><br +class="newline" /> F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">89</span>, 032804 (2014). +<!--l. 29--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a> + + + + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu9.html" >next</a>] [<a +href="mammult_docsu7.html" >prev</a>] [<a +href="mammult_docsu7.html#tailmammult_docsu7.html" >prev-tail</a>] [<a +href="mammult_docsu8.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu8.html" >up</a>] </p></div> +<!--l. 3--><p class="indent" > <a + id="tailmammult_docsu8.html"></a> +</body></html> diff --git a/doc/html/mammult_docsu9.html b/doc/html/mammult_docsu9.html new file mode 100644 index 0000000..2f3a901 --- /dev/null +++ b/doc/html/mammult_docsu9.html @@ -0,0 +1,97 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>1.1.1.0 degs_to_binary.py</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)"> +<!-- html,index=2,3,4,5,next --> +<meta name="src" content="mammult_doc.tex"> +<meta name="date" content="2015-10-19 16:26:00"> +<link rel="stylesheet" type="text/css" href="mammult_doc.css"> +</head><body +> + <!--l. 3--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu10.html" >next</a>] [<a +href="mammult_docsu8.html" >prev</a>] [<a +href="mammult_docsu8.html#tailmammult_docsu8.html" >prev-tail</a>] [<a +href="#tailmammult_docsu9.html">tail</a>] [<a +href="mammult_docsu1.html#mammult_docsu9.html" >up</a>] </p></div> + <h5 class="subsubsectionHead"><a + id="x12-110001.1.1"></a><span +class="cmtt-10x-x-109">degs</span><span +class="cmtt-10x-x-109">_to</span><span +class="cmtt-10x-x-109">_binary.py</span></h5> +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">NAME</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">degs</span><span +class="cmbx-10x-x-109">_to</span><span +class="cmbx-10x-x-109">_binary.py </span>- compute the activity vectors of all the nodes of a +multiplex. +<!--l. 3--><p class="noindent" ><span +class="cmbx-10x-x-109">SYNOPSYS</span> +<!--l. 3--><p class="indent" > <span +class="cmbx-10x-x-109">degs</span><span +class="cmbx-10x-x-109">_to</span><span +class="cmbx-10x-x-109">_binary.py </span><span +class="cmmi-10x-x-109"><</span><span +class="cmitt-10x-x-109">degree</span><span +class="cmitt-10x-x-109">_vectors</span><span +class="cmmi-10x-x-109">></span> +<!--l. 14--><p class="noindent" ><span +class="cmbx-10x-x-109">DESCRIPTION</span> +<!--l. 14--><p class="indent" > Take a file which contains, on the n-th line, the degrees at each layer of the +n-th node, (e.g., the result of the script <span +class="cmtt-10x-x-109">node</span><span +class="cmtt-10x-x-109">_degree</span><span +class="cmtt-10x-x-109">_vectors.py</span>), in the +format: +<!--l. 14--><p class="indent" >   <span +class="cmti-10x-x-109">noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_lay1 noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_lay2 ... noden</span><span +class="cmti-10x-x-109">_deg</span><span +class="cmti-10x-x-109">_layM</span> +<!--l. 14--><p class="noindent" >and compute the corresponding node activity bit-strings, where a ”1” +signals the presence of the node on that layer, while a zero indicates its +absence. +<!--l. 27--><p class="noindent" ><span +class="cmbx-10x-x-109">OUTPUT</span> +<!--l. 27--><p class="indent" > The program returns on <span +class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line is the +activity bit-string of the n-th node. Additionally, the program prints on <span +class="cmtt-10x-x-109">stderr</span> +the distribution of all activity bit-strings, in the format: +<!--l. 27--><p class="indent" >   <span +class="cmti-10x-x-109">Bn Bit-string count</span> +<!--l. 27--><p class="noindent" >Where <span +class="cmti-10x-x-109">B </span>is the number of ones in the activity bit-string (i.e., the node-activity +associated to that activity bit-string), <span +class="cmti-10x-x-109">Bit-string </span>is the activity bit-string and +<span +class="cmti-10x-x-109">count </span>is the number of times that particular activity bit-string appears in the +multiplex. +<!--l. 31--><p class="noindent" ><span +class="cmbx-10x-x-109">REFERENCE</span> +<!--l. 31--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, <span +class="cmti-10x-x-109">Phys. Rev. E </span><span +class="cmbx-10x-x-109">92</span>, 032805 (2015). +<!--l. 31--><p class="indent" > Link to paper: <a +href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span +class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a> + + + + <!--l. 4--><div class="crosslinks"><p class="noindent">[<a +href="mammult_docsu10.html" >next</a>] [<a +href="mammult_docsu8.html" >prev</a>] [<a +href="mammult_docsu8.html#tailmammult_docsu8.html" >prev-tail</a>] [<a +href="mammult_docsu9.html" >front</a>] [<a +href="mammult_docsu1.html#mammult_docsu9.html" >up</a>] </p></div> +<!--l. 4--><p class="indent" > <a + id="tailmammult_docsu9.html"></a> +</body></html> diff --git a/doc/latex/latex/dynamics/Ising/multiplex_ising.tex b/doc/latex/latex/dynamics/Ising/multiplex_ising.tex new file mode 100644 index 0000000..ec87454 --- /dev/null +++ b/doc/latex/latex/dynamics/Ising/multiplex_ising.tex @@ -0,0 +1,22 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{multiplex\_ising}} + {compute the coupled ising model in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<$T$>$ $<$J$>$ $<\gamma>$ $<h^{[1]}>$ $<h^{[2]}>$ $<p_1>$ $<p_2>$ $<num epochs>$} + +\mydescription{Compute and print the output of the ising dynamics on two coupled layers of a multiplex network. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + $T$ is the value of thermal noise in the system, $J$ the value of peer pressure, $\gamma$ the relative ratio between internal coupling and peer pressure, $h^{[1]}$ and $h^{[2]}$ the external fields acting on the two layers, $p_1$ the probability for a spin on layer $1$ at $t=0$ to be up, $p_2$ the same probability for spins on layer $2$, $num epochs$ the number of epochs for the simulation.} + +\myreturn{One line, reporting all controlling parameter, the value of consensus in layer $1$ $m^{[1]}$, the value of consensus in layer $2$ $m^{[2]}$ and the coherence $C$.} + +\myreference{\refising} diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex new file mode 100644 index 0000000..98a432b --- /dev/null +++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex @@ -0,0 +1,24 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{entropyrate2add}} + {compute the entropy rate of additive biased walks in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$} + +\mydescription{Compute and print the entropy rate of an additive biased walk in a multiplex with $2$ layers and bias parameters $b_1$ and $b_2$. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers. + + $N$ is the number of nodes, $b_1$ is the degree-biased exponent for layer $1$, $b_2$ is the degree-biased exponent for layer $2$.} + +\myreturn{One line, reporting the value of the entropy rate $h$ of an additive biased random walks with $b_1$ and $b_2$ as bias exponents, $b_1$ and $b_2$.} + +\myreference{\refbiased} diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex new file mode 100644 index 0000000..8a337f4 --- /dev/null +++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex @@ -0,0 +1,24 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{entropyrate2int}} + {compute the entropy rate of intensive biased walks in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$} + +\mydescription{Compute and print the entropy rate of an intensive biased walks in a multiplex with $2$ layers and bias parameters $b_p$ and $b_o$. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers. + + $N$ is the number of nodes, $b_p$ is the biased exponent on the participation coefficient, $b_o$ is the biased exponent on the overlapping degree.} + +\myreturn{One line, reporting the value of the entropy rate $h$ of an intensive biased random walks with $b_p$ and $b_o$ as bias exponents, $b_p$ and $b_o$.} + +\myreference{\refbiased} diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex new file mode 100644 index 0000000..7abfecd --- /dev/null +++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex @@ -0,0 +1,24 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{entropyrate2mult}} + {compute the entropy rate of multiplicative biased walks in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$} + +\mydescription{Compute and print the entropy rate of a multiplicative biased walk in a multiplex with $2$ layers and bias parameters $b_1$ and $b_2$. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers. + + $N$ is the number of nodes, $b_1$ is the degree-biased exponent for layer $1$, $b_2$ is the degree-biased exponent for layer $2$.} + +\myreturn{One line, reporting the value of the entropy rate $h$ of an multiplicative biased random walks with $b_1$ and $b_2$ as bias exponents, $b_1$ and $b_2$.} + +\myreference{\refbiased} diff --git a/doc/latex/latex/dynamics/randomwalks/statdistr2.tex b/doc/latex/latex/dynamics/randomwalks/statdistr2.tex new file mode 100644 index 0000000..09c1bc2 --- /dev/null +++ b/doc/latex/latex/dynamics/randomwalks/statdistr2.tex @@ -0,0 +1,24 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{statdistr2}} + {compute the stationary distribution of additive, multiplicative and intensive biased walks in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$} + +\mydescription{Compute and print the stationary distribution of additive, multiplicative and intensive biased walks in a multiplex with $2$ layers. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers. + + $N$ is the number of nodes, $b_1$ is the first bias exponent (the bias exponent for layer $1$ for additive and multiplicative walks, the bias exponent on the participation coefficient for intensive walks), $b_2$ is the second bias exponent (the bias exponent for layer $1$ for additive and multiplicative walks, the bias exponent on the participation coefficient for intensive walks).} + +\myreturn{N lines. In the n-th line we report the node ID, the stationary distribution of that node for additive walks with exponents $b_1$ and $b_2$, the stationary distribution for multiplicative walks with exponents $b_1$ and $b_2$, the stationary distribution for multiplicative walks with exponents $b_1$ and $b_2$, the values of the bias exponents $b_1$ and $b_2$.} + +\myreference{\refbiased} diff --git a/doc/latex/latex/models/correlations/tune_qnn_adaptive.tex b/doc/latex/latex/models/correlations/tune_qnn_adaptive.tex new file mode 100644 index 0000000..016b674 --- /dev/null +++ b/doc/latex/latex/models/correlations/tune_qnn_adaptive.tex @@ -0,0 +1,64 @@ +\myprogram{{tune\_qnn\_adaptive}} + {Construct a multiplex with prescribed inter-layer correlations.} + {$<$degs1$>$ $<$degs2$>$ $<$mu$>$ $<$eps$>$ $<$beta$>$ [RND|NAT|INV]} + +\mydescription{This programs tunes the inter-layer degree correlation + exponent $\mu$. If we consider two layers of a multiplex, + and we denote by $k$ the degree of a node on the first layer + and by $q$ the degree of the same node on the second layers, + the inter-layer degree correlation function is defined as: + + \begin{equation*} + \overline{q}(k) = \sum_{q'} q' P(q'|k) + \end{equation*} + + where $\overline{q}(k)$ is the average degree on layer $2$ + of nodes having degree $k$ on layer $1$. + + The program assumes that we want to set the degree + correlation function such that: + + \begin{equation*} + \overline{q}(k) = a k^{\mu} + \end{equation*} + + where the exponent of the power-law function is given by + the user (it is indeed the parameter \textit{mu}), and + successively adjusts the pairing between nodes at the two + layers in order to obtain a correlation function as close + as possible to the desired one. The files \textit{degs1} + and \textit{degs2} contain, respectively, the degrees of + the nodes on the first layer and on the second layer. + + The parameter \textit{eps} is the accuracy of \textit{mu}. + For instance, if \textit{mu} is set equal to -0.25 + and \textit{eps} is equal to 0.0001, the program stops when + the configuration of node pairing corresponds to a value of + the exponent $\mu$ which differs from -0.25 by less than + 0.0001. + + The parameter \textit{beta} is the typical inverse + temperature of simulated annealing. + + If no other parameter is specified, or if the last parameter + is \texttt{RND}, the program starts from a random pairing of + nodes. If the last parameter is \texttt{NAT} then the + program assumes that the initial pairing is the natural one, + where the nodes have the same ID on both layers. Finally, + if \texttt{INV} is specified, the initial pairing is the + inverse pairing, i.e. the one where node 0 on layer 1 is + paired with node N-1 on layer 2, and so on. + + } + + +\myreturn{The program prints on \texttt{stdout} a pairing, i.e. a list +of lines in the format: + +\hspace{0.5cm} \textit{IDL1 IDL2} + +where \textit{IDL1} is the ID of the node on layer 1 and \textit{IDL2} +is the corresponding ID of the same node on layer 2. +} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/models/correlations/tune_rho.tex b/doc/latex/latex/models/correlations/tune_rho.tex new file mode 100644 index 0000000..27b6079 --- /dev/null +++ b/doc/latex/latex/models/correlations/tune_rho.tex @@ -0,0 +1,45 @@ +\myprogram{{tune\_rho}} + {Construct a multiplex with prescribed inter-layer correlations.} + {$<$rank1$>$ $<$rank2$>$ $<$rho$>$ $<$eps$>$ $<$beta$>$ [RND|NAT|INV]} + +\mydescription{This programs tunes the inter-layer degree correlation + coefficient $\rho$ (Spearman's rank correlation) of two + layers, by adjusting the inter-layer pairing of nodes. The + files \textit{rank1} and \textit{rank2} are the rankings of + nodes in the first and second layer, where the n-th line of + the file contains the rank of the n-th node (the highest + ranked node has rank equal to 1). + + The parameter \textit{rho} is the desired value of the + Spearman's rank correlation coefficient, while \textit{eps} + is the accuracy of \textit{rho}. For instance, + if \textit{rho} is set equal to -0.25 and \textit{eps} is + equal to 0.0001, the program stops when the configuration of + node pairing corresponds to a value of $\rho$ which differs + from -0.25 by less than 0.0001. + + The parameter \textit{beta} is the typical inverse + temperature of simulated annealing. + + If no other parameter is specified, or if the last parameter + is \texttt{RND}, the program starts from a random pairing of + nodes. If the last parameter is \texttt{NAT} then the + program assumes that the initial pairing is the natural one, + where the nodes have the same ID on both layers. Finally, + if \texttt{INV} is specified, the initial pairing is the + inverse pairing, i.e. the one where node 0 on layer 1 is + paired with node N-1 on layer 2, and so on. + + } + + +\myreturn{The program prints on \texttt{stdout} a pairing, i.e. a list +of lines in the format: + +\hspace{0.5cm} \textit{IDL1 IDL2} + +where \textit{IDL1} is the ID of the node on layer 1 and \textit{IDL2} +is the corresponding ID of the same node on layer 2. +} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/models/growth/nibilab_linear_delay.tex b/doc/latex/latex/models/growth/nibilab_linear_delay.tex new file mode 100644 index 0000000..afbf083 --- /dev/null +++ b/doc/latex/latex/models/growth/nibilab_linear_delay.tex @@ -0,0 +1,67 @@ +\myprogram{{nibilab\_linear\_delay}} + {Multiplex linear preferential attachment model -- + Asynchronous arrival.} + {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$ + $<$c$>$ $<$d$>$ $<$beta$>$} + +\mydescription{Grow a two-layer multiplex network using the multiplex linear + preferential attachment model by Nicosia, Bianconi, Latora, + Barthelemy (NiBiLaB). + + The probability for a newly arrived node $i$ to create a + link to node $j$ on layer $1$ is: + + \begin{equation*} + \Pi_{i\to j}^{1} \propto ak\lay{1}_j + bk\lay{2}_j + \end{equation*} + + and the dual probability for $i$ to create a link to $j$ on + layer $2$ is: + + \begin{equation*} + \Pi_{i\to j}^{2} \propto ck\lay{1}_j + dk\lay{2}_j + \end{equation*} + + Each new node arrives first on layer $1$, and its replica on + the layer $2$ appears after a time delay $\tau$ sampled from + the power-law function: + + \begin{equation*} + P(\tau) \sim \tau^{-\beta} + \end{equation*} + + The (mandatory) parameters are as follows: + + \begin{itemize} + + \item \textbf{N} number of nodes in the final graph + + \item \textbf{m} number of new edges brought by each new node + + \item \textbf{m0} number of nodes in the initial seed + graph. \textit{m0} must be larger than of equal + to \textit{m}. + + \item \textbf{outfile} the name of the file which will contain the + + \item \textbf{a,b,c,d} the coefficients of the attaching probability + function + + \item \textbf{beta} the exponent of the power-law delay + function which determines the arrival of replicas on layer $2$ + + \end{itemize} + } + + +\myreturn{The program dumps on the file \texttt{outfile} the + (undirected) edge list of the resulting network. Each line of the + file is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. +} + +\myreference{\refgrowth} diff --git a/doc/latex/latex/models/growth/nibilab_linear_delay_mix.tex b/doc/latex/latex/models/growth/nibilab_linear_delay_mix.tex new file mode 100644 index 0000000..5863951 --- /dev/null +++ b/doc/latex/latex/models/growth/nibilab_linear_delay_mix.tex @@ -0,0 +1,68 @@ +\myprogram{{nibilab\_linear\_delay\_mix}} + {Multiplex linear preferential attachment model -- + Asynchronous arrival and randomly selected first layer.} + {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$ + $<$c$>$ $<$d$>$ $<$beta$>$} + +\mydescription{Grow a two-layer multiplex network using the multiplex linear + preferential attachment model by Nicosia, Bianconi, Latora, + Barthelemy (NiBiLaB). + + The probability for a newly arrived node $i$ to create a + link to node $j$ on layer $1$ is: + + \begin{equation*} + \Pi_{i\to j}^{1} \propto ak\lay{1}_j + bk\lay{2}_j + \end{equation*} + + and the dual probability for $i$ to create a link to $j$ on + layer $2$ is: + + \begin{equation*} + \Pi_{i\to j}^{2} \propto ck\lay{1}_j + dk\lay{2}_j + \end{equation*} + + Each new node arrives on one of the two layers, chosen + uniformly at random, and its replica on the other layer + appears after a time delay $\tau$ sampled from the power-law + function: + + \begin{equation*} + P(\tau) \sim \tau^{-\beta} + \end{equation*} + + The (mandatory) parameters are as follows: + + \begin{itemize} + + \item \textbf{N} number of nodes in the final graph + + \item \textbf{m} number of new edges brought by each new node + + \item \textbf{m0} number of nodes in the initial seed + graph. \textit{m0} must be larger than of equal + to \textit{m}. + + \item \textbf{outfile} the name of the file which will contain the + + \item \textbf{a,b,c,d} the coefficients of the attaching probability + function + + \item \textbf{beta} the exponent of the power-law delay + function which determines the arrival of replicas on layer $2$ + + \end{itemize} + } + + +\myreturn{The program dumps on the file \texttt{outfile} the + (undirected) edge list of the resulting network. Each line of the + file is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. +} + +\myreference{\refgrowth} diff --git a/doc/latex/latex/models/growth/nibilab_linear_delta.tex b/doc/latex/latex/models/growth/nibilab_linear_delta.tex new file mode 100644 index 0000000..27ebbd0 --- /dev/null +++ b/doc/latex/latex/models/growth/nibilab_linear_delta.tex @@ -0,0 +1,57 @@ +\myprogram{{nibilab\_linear\_delta}} + {Multiplex linear preferential attachment model -- + Synchronous arrival.} + {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$ $<$c$>$ $<$d$>$} + +\mydescription{Grow a two-layer multiplex network using the multiplex linear + preferential attachment model by Nicosia, Bianconi, Latora, + Barthelemy (NiBiLaB). + + The probability for a newly arrived node $i$ to create a + link to node $j$ on layer $1$ is: + + \begin{equation*} + \Pi_{i\to j}^{1} \propto ak\lay{1}_j + bk\lay{2}_j + \end{equation*} + + and the dual probability for $i$ to create a link to $j$ on + layer $2$ is: + + \begin{equation*} + \Pi_{i\to j}^{2} \propto ck\lay{1}_j + dk\lay{2}_j + \end{equation*} + + Each new node arrives at the same time on both layers. + + The (mandatory) parameters are as follows: + + \begin{itemize} + + \item \textbf{N} number of nodes in the final graph + + \item \textbf{m} number of new edges brought by each new node + + \item \textbf{m0} number of nodes in the initial seed + graph. \textit{m0} must be larger than of equal + to \textit{m}. + + \item \textbf{outfile} the name of the file which will contain the + + \item \textbf{a,b,c,d} the coefficients of the attaching probability + function + + \end{itemize} + } + + +\myreturn{The program dumps on the file \texttt{outfile} the + (undirected) edge list of the resulting network. Each line of the + file is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. +} + +\myreference{\refgrowth} diff --git a/doc/latex/latex/models/growth/nibilab_linear_random_times.tex b/doc/latex/latex/models/growth/nibilab_linear_random_times.tex new file mode 100644 index 0000000..5f1c0fe --- /dev/null +++ b/doc/latex/latex/models/growth/nibilab_linear_random_times.tex @@ -0,0 +1,63 @@ +\myprogram{{nibilab\_linear\_random\_times}} + {Multiplex linear preferential attachment model -- + Asynchronous arrival with randomly sampled arrival times on + layer 2.} + {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$ + $<$c$>$ $<$d$>$ } + +\mydescription{Grow a two-layer multiplex network using the multiplex linear + preferential attachment model by Nicosia, Bianconi, Latora, + Barthelemy (NiBiLaB). + + The probability for a newly arrived node $i$ to create a + link to node $j$ on layer $1$ is: + + \begin{equation*} + \Pi_{i\to j}^{1} \propto ak\lay{1}_j + bk\lay{2}_j + \end{equation*} + + and the dual probability for $i$ to create a link to $j$ on + layer $2$ is: + + \begin{equation*} + \Pi_{i\to j}^{2} \propto ck\lay{1}_j + dk\lay{2}_j + \end{equation*} + + Each new node arrives on layer $1$, but its replica on the + other layer appears at a uniformly chosen random time in + $[m0+1; N]$. + + + The (mandatory) parameters are as follows: + + \begin{itemize} + + \item \textbf{N} number of nodes in the final graph + + \item \textbf{m} number of new edges brought by each new node + + \item \textbf{m0} number of nodes in the initial seed + graph. \textit{m0} must be larger than of equal + to \textit{m}. + + \item \textbf{outfile} the name of the file which will contain the + + \item \textbf{a,b,c,d} the coefficients of the attaching probability + function + + + \end{itemize} + } + + +\myreturn{The program dumps on the file \texttt{outfile} the + (undirected) edge list of the resulting network. Each line of the + file is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. +} + +\myreference{\refgrowth} diff --git a/doc/latex/latex/models/growth/nibilab_nonlinear.tex b/doc/latex/latex/models/growth/nibilab_nonlinear.tex new file mode 100644 index 0000000..2e48a18 --- /dev/null +++ b/doc/latex/latex/models/growth/nibilab_nonlinear.tex @@ -0,0 +1,60 @@ +\myprogram{{nibilab\_nonlinear}} + {Multiplex non-linear preferential attachment model -- + Synchronous arrival.} + {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$alpha$>$ $<$beta$>$} + +\mydescription{Grow a two-layer multiplex network using the multiplex non-linear + preferential attachment model by Nicosia, Bianconi, Latora, + Barthelemy (NiBiLaB). + + The probability for a newly arrived node $i$ to create a + link to node $j$ on layer $1$ is: + + \begin{equation*} + \Pi_{i\to j}^{1} \propto \frac{\left(k\lay{1}_j\right)^{\alpha}} + {\left(k\lay{2}_j\right)^{\beta}} + \end{equation*} + + and the dual probability for $i$ to create a link to $j$ on + layer $2$ is: + + \begin{equation*} + \Pi_{i\to j}^{2} \propto \frac{\left(k\lay{2}_j\right)^{\alpha}} + {\left(k\lay{1}_j\right)^{\beta}} + \end{equation*} + + Each node arrives simultaneously on both layers. + + + The (mandatory) parameters are as follows: + + \begin{itemize} + + \item \textbf{N} number of nodes in the final graph + + \item \textbf{m} number of new edges brought by each new node + + \item \textbf{m0} number of nodes in the initial seed + graph. \textit{m0} must be larger than of equal + to \textit{m}. + + \item \textbf{outfile} the name of the file which will contain the + + \item \textbf{alpha, beta} exponents of of the attaching probability + function + + \end{itemize} + } + + +\myreturn{The program dumps on the file \texttt{outfile} the + (undirected) edge list of the resulting network. Each line of the + file is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. +} + +\myreference{\refgrowth} diff --git a/doc/latex/latex/models/growth/node_deg_over_time.tex b/doc/latex/latex/models/growth/node_deg_over_time.tex new file mode 100644 index 0000000..351045e --- /dev/null +++ b/doc/latex/latex/models/growth/node_deg_over_time.tex @@ -0,0 +1,50 @@ +\myprogram{{node\_deg\_over\_time.py}} + {Time evolution of the degree of a node in a growing graph.} + {$<$layer$>$ $<$arrival\_times$>$ $<$node\_id$>$ + [$<$node\_id$>$ ...]} + +\mydescription{Compute the degree $k_{i}(t)$ of node $i$ in a growing + network as a function of time. The file \textit{layer} + contains the edge list of the final network. Each line of + the file is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{arrival\_times} is a list of node arrival times, in + the format: + + \hspace{0.5cm} \textit{time\_i node\_i} + + where \textit{time\_i} is the time at which \textit{node\_i} arrived + in the graph. Notice that \textit{time\_i} must be an integer in the + range [0, N-1], where N is the total number of nodes in the final + graph. + + The third parameter \textit{node\_id} is the ID of the node whose + degree over time will be printed on output. If more than + one \textit{node\_id} is provided, the degrees over time of all the + corresponding nodes are printed on output. + } + + +\myreturn{The program prints on \texttt{stdout} a list of lines in the + format: + + \hspace{0.5cm} \textit{t kit} + + where \textit{kit} is the degree of node \textit{i} at + time \textit{t}. The first line of output is in the format: + + \hspace{0.5cm} \textit{\#\#\#\# node\_id} + + where \textit{node\_id} is the ID of node \textit{i}. + + If more than one \textit{node\_id}s is provided as input, the program + prints the degree over time of all of them, sequentially. + +} + +\myreference{\refgrowth} diff --git a/doc/latex/latex/models/nullmodels/model_MDM.tex b/doc/latex/latex/models/nullmodels/model_MDM.tex new file mode 100644 index 0000000..dd754b8 --- /dev/null +++ b/doc/latex/latex/models/nullmodels/model_MDM.tex @@ -0,0 +1,37 @@ +\myprogram{{model\_MDM.py}} + {Multi-activity Deterministic Model.} + {$<$Bi\_file$>$ $<$M$>$} + +\mydescription{This is the Multi-activity Deterministic Model (MDM). + In this model each node $i$ is considered active if it was + active in the reference multiplex, maintains the same value + of node activity $B_i$ (i.e., the number of layers in which + it was active) and is associated an activity vector sampled + uniformly at random from the $M\choose{B_i}$ possible + activity vectors with $B_i$ non-null entries. + + The file \textit{Bi\_file} is in the format: + + \hspace{0.5cm} \textit{Bi N(Bi)} + + where \textit{Bi} is a value of node activity + and \textit{N(Bi)} is the number of nodes which had node + activity equaly to \textit{Bi} in the reference multiplex. + + The parameter \textit{M} is the number of layers in the + multiplex. +} + + +\myreturn{The program prints on \texttt{stdout} a distribution of + bit-strings, in the format: + + \hspace{0.5cm} \textit{Bi bitstring count} + + where \textit{bitstring} is the activity + bitstring, \textit{Bi} is the number of non-zero entries + of \textit{bitstring} and \textit{count} is the number of + times that \textit{bitstrings} appear in the null model.} + + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/models/nullmodels/model_MSM.tex b/doc/latex/latex/models/nullmodels/model_MSM.tex new file mode 100644 index 0000000..e3c8abf --- /dev/null +++ b/doc/latex/latex/models/nullmodels/model_MSM.tex @@ -0,0 +1,38 @@ +\myprogram{{model\_MSM.py}} + {Multi-activity Stochastic Model.} + {$<$node\_Bi\_file$>$ $<$M$>$} + +\mydescription{This is the Multi-activity Stochastic Model (MSM). + In this model each node $i$ is considered active if it was + active in the reference multiplex, and is activated on + each layer with a probability equal to $B_i/M$ where $B_i$ + was the activity of node $i$ in the reference multiplex. + + The file \textit{node\_Bi\_file} is in the format: + + \hspace{0.5cm} \textit{node\_i Bi)} + + where \textit{Bi} is the value of node activity + of \textit{node\_i} in the reference multiplex. + + + The parameter \textit{M} is the number of layers in the + multiplex. +} + +\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the + format: + + \hspace{0.5cm} \textit{node\_i layer\_i} + + where \textit{node\_i} is the ID of a node and \textit{layre\_i} is + the ID of a layer. This list indicates which nodes are active in + which layer. For instance, the line: + + \hspace{0.5cm} \textit{24 3} + + indicates that the node with ID \textit{24} is active on + layer \textit{3}. +} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/models/nullmodels/model_hypergeometric.tex b/doc/latex/latex/models/nullmodels/model_hypergeometric.tex new file mode 100644 index 0000000..0315c7b --- /dev/null +++ b/doc/latex/latex/models/nullmodels/model_hypergeometric.tex @@ -0,0 +1,33 @@ +\myprogram{{model\_hypergeometric.py}} + {Hypergeometric node activity null model.} + {$<$layer\_N\_file$>$ $<$N$>$} + +\mydescription{This is the hypergeometric model of node activation. In + this model each layer has exactly the same number of active + node of a reference multiplex network, but nodes on each + layer are activated uniformly at random, thus destroying all + inter-layer activity correlation patterns. + + The file \textit{layer\_N\_file} reports on the n-th line + the number of active nodes on the n-th layer (starting from + zero). The second parameter \textit{N} is the total number + of active nodes in the multiplex. + } + + +\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the + format: + + \hspace{0.5cm} \textit{node\_i layer\_i} + + where \textit{node\_i} is the ID of a node and \textit{layre\_i} is + the ID of a layer. This list indicates which nodes are active in + which layer. For instance, the line: + + \hspace{0.5cm} \textit{24 3} + + indicates that the node with ID \textit{24} is active on + layer \textit{3}. +} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/models/nullmodels/model_layer_growth.tex b/doc/latex/latex/models/nullmodels/model_layer_growth.tex new file mode 100644 index 0000000..9c0bb12 --- /dev/null +++ b/doc/latex/latex/models/nullmodels/model_layer_growth.tex @@ -0,0 +1,46 @@ +\myprogram{{model\_layer\_growth.py}} + {Layer growth with preferential activation model.} + {$<$layer\_N\_file$>$ $<$N$>$ $<$M0$>$ $<$A$>$ [RND]} + +\mydescription{This is the model of layer growth with preferential + node activation. In this model an entire new layer arrives + at time $t$ and a number of nodes $N_t$ is activated ($N\_t$ + is equal to the number of nodes active on that layer in the + reference multiplex). Then, each node $i$ of the new layer + is activated with a probability: + + \begin{equation*} + P_i(t) \propto A + B_i(t) + \end{equation*} + + where $B_i(t)$ is the activity of node $i$ at time $t$ + (i.e., the number of layers in which node $i$ is active at + time $t$) while $A>0$ is an intrinsic attractiveness. + + The file \textit{layer\_N\_file} reports on the n-th line + the number of active nodes on the n-th layer. + + The parameter \textit{N} is the number of nodes in the + multiplex, \textit{M0} is the number of layers in the + initial network, \textit{A} is the value of + node attractiveness. + + If the user specifies \texttt{RND} as the last parameter, + the sequence of layers is } + +\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the + format: + + \hspace{0.5cm} \textit{node\_i layer\_i} + + where \textit{node\_i} is the ID of a node and \textit{layre\_i} is + the ID of a layer. This list indicates which nodes are active in + which layer. For instance, the line: + + \hspace{0.5cm} \textit{24 3} + + indicates that the node with ID \textit{24} is active on + layer \textit{3}. +} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/activity/degs_to_activity_overlap.tex b/doc/latex/latex/structure/activity/degs_to_activity_overlap.tex new file mode 100644 index 0000000..6e1908f --- /dev/null +++ b/doc/latex/latex/structure/activity/degs_to_activity_overlap.tex @@ -0,0 +1,29 @@ +\myprogram{{degs\_to\_activity\_overlap.py}} + {compute the activity and the total (overlapping) degree of + all the nodes of a multiplex.} + {$<$degree\_vectors$>$} + +\mydescription{Take a file which contains, on the n-th line, the degrees at each + layer of the n-th node, (e.g., the result of the + script \texttt{node\_degree\_vectors.py}), in the format: + + \hspace{0.5cm}\textit{noden\_deg\_lay1 noden\_deg\_lay2 ... noden\_deg\_layM} + + \noindent and compute the activity (i.e., the number of layers in + which a node is not isolated) and the total (overlapping) degree of + each node.} + +\myreturn{The program prints on \texttt{stdout} a list of lines, where + the n-th line contains the activity and the total degree of the n-th + nodem in the format: + + \hspace{0.5cm}\textit{noden\_activity noden\_tot\_deg} + + \noindent As usual, the program assumes that node IDs start from zero + and proceed sequentially, without gaps, i.e., if a node ID is not + present in any of the layer files given as input, the program + considers it as being isolated on all the layers. + } + +\myreference{\refcorrelations} + diff --git a/doc/latex/latex/structure/activity/degs_to_binary.tex b/doc/latex/latex/structure/activity/degs_to_binary.tex new file mode 100644 index 0000000..7441b2d --- /dev/null +++ b/doc/latex/latex/structure/activity/degs_to_binary.tex @@ -0,0 +1,32 @@ +\myprogram{{degs\_to\_binary.py}} + {compute the activity vectors of all the nodes of a multiplex.} + {$<$degree\_vectors$>$} + +\mydescription{Take a file which contains, on the n-th line, the degrees at each + layer of the n-th node, (e.g., the result of the + script \texttt{node\_degree\_vectors.py}), in the format: + + \hspace{0.5cm}\textit{noden\_deg\_lay1 noden\_deg\_lay2 ... noden\_deg\_layM} + + \noindent and compute the corresponding node activity bit-strings, + where a "1" signals the presence of the node on that layer, while a + zero indicates its absence. +} + +\myreturn{The program returns on \texttt{stdout} a list of lines, + where the n-th line is the activity bit-string of the n-th + node. Additionally, the program prints on \texttt{stderr} the + distribution of all activity bit-strings, in the format: + + \hspace{0.5cm}\textit{Bn Bit-string count} + + \noindent Where \textit{B} is the number of ones in the activity + bit-string (i.e., the node-activity associated to that activity + bit-string), \textit{Bit-string} is the activity bit-string + and \textit{count} is the number of times that particular activity + bit-string appears in the multiplex.} + + + +\myreference{\refcorrelations} + diff --git a/doc/latex/latex/structure/activity/hamming_dist.tex b/doc/latex/latex/structure/activity/hamming_dist.tex new file mode 100644 index 0000000..3af188f --- /dev/null +++ b/doc/latex/latex/structure/activity/hamming_dist.tex @@ -0,0 +1,31 @@ +\myprogram{{hamming\_dist.py}} + {compute the normalised Hamming distance between all the pairs of + layers of a multiplex.} + {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]} + +\mydescription{Compute and print on output the normalised Hamming distance + $H_{\alpha, \beta}$ (i.e., the fraction of nodes which are active on + either of the layers, but not on both) between all pairs of + layers. The layers are given as input in the + files \textit{layer1}, \textit{layer2}, etc. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines, in + the format: + + \hspace{0.5cm} \textit{layer1 layer2 hamm} + + \noindent where \textit{layer1} and \textit{layer2} are the IDs of + the layers, and \textit{hamm} is the value of the normalised Haming + distance $H_{layer1, layer2}$. Layers IDs start from zero, are are + associated to the layers in the same order in which the layer files + are provided on the command line.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/activity/layer_activity.tex b/doc/latex/latex/structure/activity/layer_activity.tex new file mode 100644 index 0000000..34fcdd2 --- /dev/null +++ b/doc/latex/latex/structure/activity/layer_activity.tex @@ -0,0 +1,25 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{layer\_activity.py}} + {compute the activity of the layers of a multiplex, i.e. the + number of active nodes on each layer.} + {$<$layer1$>$ [$<$layer2$>$ ...]} + +\mydescription{Compute and print on output the activity of the layers + of a multiplex network, where the layers are given as input in the + files \textit{layer1}, \textit{layer2}, etc. + + Each file contains the (undirected) edge list of a layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{A listof lines, where the n-th line is the value of activity + of the n-th layer, starting from \textbf{0}.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/activity/layer_activity_vectors.tex b/doc/latex/latex/structure/activity/layer_activity_vectors.tex new file mode 100644 index 0000000..f0c2cd6 --- /dev/null +++ b/doc/latex/latex/structure/activity/layer_activity_vectors.tex @@ -0,0 +1,27 @@ +\myprogram{{layer\_activity\_vectors.py}} + {compute the activity vectors of all the layers of a multiplex.} + {$<$layer1$>$ [$<$layer2$>$ ...]} + +\mydescription{Compute and print on output the activity vectors of the + layers of a multiplex network, where the layers are given as input + in the files \textit{layer1}, \textit{layer2}, etc. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines, where + the n-th line contains the activity vector of the n-th layer, i.e. a + bit-string where each bit is set to ``1'' if the corresponding node + is active on the n-th layer, and to ``0'' otherwise. + + \noindent As usual, node IDs start from zero and proceed + sequentially, without gaps, i.e., if a node ID is not present in any + of the layer files given as input, the program considers it as being + isolated on all the layers.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/activity/multiplexity.tex b/doc/latex/latex/structure/activity/multiplexity.tex new file mode 100644 index 0000000..b5c5506 --- /dev/null +++ b/doc/latex/latex/structure/activity/multiplexity.tex @@ -0,0 +1,30 @@ +\myprogram{{multiplexity.py}} + {compute the pairwise multiplexity between all the pairs of + layers of a multiplex.} + {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]} + +\mydescription{Compute and print on output the pairwise multiplexity + $Q_{\alpha, \beta}$ (i.e., the fraction of nodes active on both + layers) between all pairs of layers. The layers are given as + input in the files \textit{layer1}, \textit{layer2}, etc. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines, in + the format: + + \hspace{0.5cm} \textit{layer1 layer2 mult} + + \noindent where \textit{layer1} and \textit{layer2} are the IDs of + the layers, and \textit{mult} is the value of the multiplexity + $Q_{layer1, layer2}$. Layers IDs start from zero, are are associated + to the layers in the same order in which the layer files are + provided on the command line.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/activity/node_activity.tex b/doc/latex/latex/structure/activity/node_activity.tex new file mode 100644 index 0000000..882233d --- /dev/null +++ b/doc/latex/latex/structure/activity/node_activity.tex @@ -0,0 +1,25 @@ +%%% +%%% node_activity +%%% +\myprogram{{node\_activity.py}} + {compute the activity of the nodes of a multiplex, i.e. the + number of layers where each node is not isolated.} + {$<$layer1$>$ [$<$layer2$>$ ...]} + +\mydescription{Compute and print on output the activity of the nodes + of a multiplex network, whose layers are given as input in the files + \textit{layer1}, \textit{layer2}, etc. + + Each file contains the (undirected) edge list of a layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{A list of lines, where the n-th line is the value of activity + of the n-th node, starting from \textbf{0}.} + +\myreference{\refcorrelations} + diff --git a/doc/latex/latex/structure/activity/node_activity_vectors.tex b/doc/latex/latex/structure/activity/node_activity_vectors.tex new file mode 100644 index 0000000..ca9301d --- /dev/null +++ b/doc/latex/latex/structure/activity/node_activity_vectors.tex @@ -0,0 +1,28 @@ +\myprogram{{node\_activity\_vectors.py}} + {compute the activity vectors of all the nodes of a multiplex.} + {$<$layer1$>$ [$<$layer2$>$ ...]} + +\mydescription{Compute and print on output the activity vectors of the + nodes of a multiplex network, whose layers are given as input in the + files \textit{layer1}, \textit{layer2}, etc. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines, where + the n-th line contains the activity vector of the n-th node, i.e. a + bit-string where each bit is set to ``1'' if the node is active on + the corresponding layer, and to ``0'' otherwise. + + \noindent As usual, node IDs start from zero and proceed + sequentially, without gaps, i.e., if a node ID is not present in any + of the layer files given as input, the program considers it as being + isolated on all the layers, and will print on output a bit-string of + zeros.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/activity/node_degree_vectors.tex b/doc/latex/latex/structure/activity/node_degree_vectors.tex new file mode 100644 index 0000000..c86f083 --- /dev/null +++ b/doc/latex/latex/structure/activity/node_degree_vectors.tex @@ -0,0 +1,30 @@ +\myprogram{{node\_degree\_vectors.py}} + {compute the degree vectors of all the nodes of a multiplex network} + {$<$layer1$>$ [$<$layer2$>$ ...]} + +\mydescription{Compute and print on output the degree vectors of all + the nodes of a multiplex network, whose layers are given as + input in the files \textit{layer1}, \textit{layer2}, etc. + + Each file contains the (undirected) edge list of a layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{A list of lines, where the n-th line is the + vector of degrees of the n-th node, in the format: + + \hspace{0.5cm}\textit{noden\_deg\_lay1 noden\_deg\_lay2 ... noden\_deg\_layM} + + \noindent As usual, node IDs start from zero and proceed + sequentially, without gaps, i.e., if a node ID is not present in any + of the layer files given as input, the program considers it as being + isolated on all the layers. + +} + +\myreference{\refgrowth\\ \\ \indent \refmetrics} + diff --git a/doc/latex/latex/structure/correlations/compute_pearson.tex b/doc/latex/latex/structure/correlations/compute_pearson.tex new file mode 100644 index 0000000..8202753 --- /dev/null +++ b/doc/latex/latex/structure/correlations/compute_pearson.tex @@ -0,0 +1,28 @@ +\myprogram{{compute\_pearson.py}} + {compute the Pearson's linear correlation coefficient + between two node properties.} + {$<$file1$>$ $<$file2$>$} + +\mydescription{Compute the Pearson's linear correlation coefficient + between two sets of (either integer- or real-valued) node + properties provided in the input files \textit{file1} + and \textit{file2}. Each input file contains a list of + lines, where the n-th line contains the value of a node + property for the n-th node. For instance, \textit{file1} + and \textit{file2} might contain the degrees of nodes at two + distinct layers of a multiplex. However, the program is + pretty general and can be used to compute the Pearson's + correlation coeffcient between any pairs of node properties. + } + +\myreturn{The program prints on \texttt{stdout} the value of the + Pearson's linear correlation coefficient between the two + sets of node properties. +} + +\myreference{\refcorrelations + + \refgrowth + + \refnonlinear +} diff --git a/doc/latex/latex/structure/correlations/compute_rho.tex b/doc/latex/latex/structure/correlations/compute_rho.tex new file mode 100644 index 0000000..957b04c --- /dev/null +++ b/doc/latex/latex/structure/correlations/compute_rho.tex @@ -0,0 +1,32 @@ +\myprogram{{compute\_rho.py}} + {compute the Spearman's rank correlation coefficient $\rho$ + between two rankings.} {$<$file1$>$ $<$file2$>$} + +\mydescription{Compute the Spearman's rank correlation coefficient + $\rho$ between two rankings provided in the input + files \textit{file1} and \textit{file2}. Each input file + contains a list of lines, where the n-th line contains the + value of rank of the n-th node. For instance, \textit{file1} + and \textit{file2} might contain the ranks of nodes induced + by the degree sequences of two distinct layers of a + multiplex. + + However, the program is pretty general and can be used to + compute the Spearman's rank correlation coefficient between + any generic pair of rankings. + + N.B.: A C implementation of this program, with the same + interface is also available in the executable + file \texttt{compute\_rho}.} + + +\myreturn{The program prints on \texttt{stdout} the value of the + Spearman's rank correlation coefficient $\rho$ between the + two rankings provided as input. } + +\myreference{\refcorrelations + + \refgrowth + + \refnonlinear + } diff --git a/doc/latex/latex/structure/correlations/compute_tau.tex b/doc/latex/latex/structure/correlations/compute_tau.tex new file mode 100644 index 0000000..e6e8589 --- /dev/null +++ b/doc/latex/latex/structure/correlations/compute_tau.tex @@ -0,0 +1,31 @@ +\myprogram{{compute\_tau.py}} + {compute the Kendall's rank correlation coefficient $\tau_b$ + between two rankings.} {$<$file1$>$ $<$file2$>$} + +\mydescription{Compute the Kendall's rank correlation coefficient + $\tau_b$ between two rankings provided in the input + files \textit{file1} and \textit{file2}. Each input file + contains a list of lines, where the n-th line contains the + value of rank of the n-th node. For instance, \textit{file1} + and \textit{file2} might contain the ranks of nodes induced + by the degree sequences of two distinct layers of a + multiplex. + + However, the program is pretty general and can be used to + compute the Kendall's rank correlation coefficient between + any generic pair of rankings. + + N.B.: This implementation takes properly into account rank + ties.} + + +\myreturn{The program prints on \texttt{stdout} the value of the + Kendall's rank correlation coefficient $\tau_b$ between the + two rankings provided as input. } + +\myreference{\refcorrelations + + \refgrowth + + \refnonlinear +} diff --git a/doc/latex/latex/structure/correlations/dump_k_q.tex b/doc/latex/latex/structure/correlations/dump_k_q.tex new file mode 100644 index 0000000..35aef8d --- /dev/null +++ b/doc/latex/latex/structure/correlations/dump_k_q.tex @@ -0,0 +1,42 @@ +M\myprogram{{dump\_k\_q}} + {compute the degree sequences of two layers of a multiplex.} + {$<$layer1$>$ $<$layer2$>$ $<$pairing$>$} + +\mydescription{Compute and dump on \texttt{stdout} the degree + sequences of two layers of a multiplex. The input + files \textit{layer1} and \textit{layer2} contain the + (undirected) edge lists of the two layers, and each line is + in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The third file \textit{pairing} is a list of lines in the format: + + \hspace{0.5cm} \textit{IDL1 IDL2} + + where \textit{IDL1} is the ID of a node on layer $1$ + and \textit{IDL2} is the ID of the same node on layer $2$. For + instance, the line: + + \hspace{0.5cm} \textit{5 27} + + indicates that node $5$ on layer $1$ has ID $27$ on layer $2$. } + + +\myreturn{The program prints on \texttt{stdout} the degree of each +node on the two layers, in the format: + +\hspace{0.5cm} \textit{ki qi} + +where \textit{ki} is the degree of node \textit{i} on layer $1$ +and \textit{qi} is the degree of node \textit{i} on layer $2$.} + +\myreference{\refcorrelations + + \refgrowth + + \refnonlinear + } diff --git a/doc/latex/latex/structure/correlations/fit_knn.tex b/doc/latex/latex/structure/correlations/fit_knn.tex new file mode 100644 index 0000000..cb90c2b --- /dev/null +++ b/doc/latex/latex/structure/correlations/fit_knn.tex @@ -0,0 +1,50 @@ +\myprogram{{fit\_knn}} + {power-law fit of the inter-layer degree correlation + function.} + {$<$filein$>$ $<$alpha$>$} + +\mydescription{Perform a power-law fit of the inter-layer degree + correlation function: + + \begin{equation*} + \overline{q}(k) = \frac{1}{N_{q}}\sum_{q'} q' P(q'|k) + \end{equation*} + + where $k$ is the degree of a node on layer $1$, $q$ is the + degree on layer $2$ and $P(q|k)$ is the probability that a + node with degree $k$ on layer $1$ has degree $q$ on layer + $2$. The program assumes that $\overline{q}(k)$ can be + written in the form $a k^{b}$, and computes the two + parameters $a$ and $b$ through a linear fit of the log-log + plot of $\overline{q}(k)$. + + The input file \textit{filein} contains a list of lines in + the format: + + \hspace{0.5cm} \textit{ki qi} + + where \textit{ki} is the degree of node $i$ at layer $1$ + and \textit{qi} is the degree of node $i$ at layer $2$. + + The second parameter \textit{alpha} is the ratio of the + progression used to generate the exponentially-distributed + bins for the log-log plot. Typical values of \textit{alpha} + are between $1.1$ and $2.0$. + + + N.B.: The exponent $b$ computed with this method is known to + be inaccurate. +} + + + +\myreturn{The program prints on \texttt{stdout} the values of the + parameters $a$ and $b$ of the power-law fit $\overline{q}(k) + = a k^{b}$.} + +\myreference{\refcorrelations + + \refgrowth + + \refnonlinear + } diff --git a/doc/latex/latex/structure/correlations/knn_q_from_degrees.tex b/doc/latex/latex/structure/correlations/knn_q_from_degrees.tex new file mode 100644 index 0000000..cab0905 --- /dev/null +++ b/doc/latex/latex/structure/correlations/knn_q_from_degrees.tex @@ -0,0 +1,64 @@ +\myprogram{{knn\_q\_from\_degrees.py}} + {compute the inter-layer degree-degree correlation function.} + {$<$filein$>$} + +\mydescription{Compute the inter-layer degree + correlation functions for two layers of a multiplex, using + the degrees of the nodes specified in the input file. The + format of the input file is as follows + +\hspace{0.5cm} \textit{ki qi} + +where \textit{ki} and \textit{qi} are, respectively, the degree at +layer 1 and the degree at layer 2 of node \textit{i}. + + If we consider two layers of a multiplex, and we denote by + $k$ the degree of a node on the first layer and by $q$ the + degree of the same node on the second layers, the + inter-layer degree correlation function is defined as + + \begin{equation*} + \overline{k}(q) = \frac{1}{N_{k}}\sum_{k'} k' P(k'|q) + \end{equation*} + + where $P(k'|q)$ is the probability that a node with degree + $q$ on the second layer has degree equal to $k'$ on the + first layer, and $N_k$ is the number of nodes with degree + $k$ on the first layer. The quantity $\overline{k}(q)$ is + the expected degree at layer $1$ of node that have degree + equal to $q$ on layer $2$. The dual quantity: + + \begin{equation*} + \overline{q}(k) = \frac{1}{N_{q}}\sum_{q'} q' P(q'|k) + \end{equation*} + + is the average degree on layer $2$ of nodes having degree + $k$ on layer $1$. +} + + +\myreturn{The program prints on \texttt{stdout} a list of lines in + the format: + + \hspace{0.5cm} \textit{k $\overline{q}(k)$} + + where \textit{k} is the degree on layer $1$ and + $\overline{q}(k)$ is the average degree on layer $2$ of + nodes having degree equal to $k$ on layer $1$. + + The program also prints on \texttt{stderr} a list of lines in + the format: + + \hspace{0.5cm} \textit{q $\overline{k}(q)$} + + where \textit{q} is the degree on layer $2$ and + $\overline{k}(q)$ is the average degree on layer $1$ of + nodes having degree equal to $q$ on layer $2$. + } + +\myreference{\refcorrelations + + \refgrowth + + \refnonlinear + } diff --git a/doc/latex/latex/structure/correlations/knn_q_from_layers.tex b/doc/latex/latex/structure/correlations/knn_q_from_layers.tex new file mode 100644 index 0000000..f124e55 --- /dev/null +++ b/doc/latex/latex/structure/correlations/knn_q_from_layers.tex @@ -0,0 +1,80 @@ +\myprogram{{knn\_q\_from\_layers.py}} + {compute intra-layer and inter-layer degree-degree + correlation coefficients.} {$<$layer1$>$ $<$layer2$>$} + +\mydescription{Compute the intra-layer and the inter-layer degree + correlation functions for two layers given as input. The + intra-layer degree correlation function quantifies the + presence of degree-degree correlations in a single layer + network, and is defined as: + + \begin{equation*} + \avg{k_{nn}(k)} = \frac{1}{k N_k}\sum_{k'}k'P(k'|k) + \end{equation*} + + where $P(k'|k)$ is the probability that a neighbour of a + node with degree $k$ has degree $k'$, and $N_k$ is the + number of nodes with degree $k$. The quantity + $\avg{k_{nn}(k)}$ is the average degree of the neighbours of + nodes having degree equal to $k$. + + If we consider two layers of a multiplex, and we denote by + $k$ the degree of a node on the first layer and by $q$ the + degree of the same node on the second layers, the + inter-layer degree correlation function is defined as + + \begin{equation*} + \overline{k}(q) = \sum_{k'} k' P(k'|q) + \end{equation*} + + where $P(k'|q)$ is the probability that a node with degree + $q$ on the second layer has degree equal to $k'$ on the + first layer, and $N_q$ is the number of nodes with degree + $q$ on the second layer. The quantity $\overline{k}(q)$ is + the expected degree at layer $1$ of node that have degree + equal to $q$ on layer $2$. The dual quantity: + + \begin{equation*} + \overline{q}(k) = \sum_{q'} q' P(q'|k) + \end{equation*} + + is the average degree on layer $2$ of nodes having degree + $k$ on layer $1$. +} + + +\myreturn{The program creates two output files, respectively called + +\hspace{0.5cm} \textit{file1\_file2\_k1} + +and + +\hspace{0.5cm} \textit{file1\_file2\_k2} + +The first file contains a list of lines in the format: + +\hspace{0.5cm} \textit{k $\avg{k_{nn}(k)}$ $\sigma_k$ +$\overline{q}(k)$ $\sigma_{\overline{q}}$} + +where $k$ is the degree at first layer, $\avg{k_{nn}(k)}$ is the +average degree of the neighbours at layer $1$ of nodes having degree +$k$ at layer $1$, $\sigma_k$ is the standard deviation associated to +$\avg{k_{nn}(k)}$, $\overline{q}(k)$ is the average degree at layer +$2$ of nodes having degree equal to $k$ at layer $1$, and +$\sigma_{\overline{q}}$ is the standard deviation associated to +$\overline{q}(k)$. + +The second file contains a similar list of lines, in the format: + +\hspace{0.5cm} \textit{q $\avg{q_{nn}(q)}$ $\sigma_q$ +$\overline{k}(q)$ $\sigma_{\overline{k}}$} + +with obvious meaning. +} + +\myreference{\refcorrelations + + \refgrowth + + \refnonlinear + } diff --git a/doc/latex/latex/structure/correlations/rank_nodes.tex b/doc/latex/latex/structure/correlations/rank_nodes.tex new file mode 100644 index 0000000..b1a970a --- /dev/null +++ b/doc/latex/latex/structure/correlations/rank_nodes.tex @@ -0,0 +1,19 @@ +\myprogram{{rank\_nodes.py}} + {rank the nodes of a layer according to a given structural + descriptor.} {$<$prop\_file$>$} + +\mydescription{Get a file as input, whose n-th line corresponds to the value of a + certain property of the n-th node, and rank the nodes according to + that property, taking into account ranking ties properly. + + For example, if \textit{propfile} contains the degrees of the nodes + at a certain layer of the multiplex, the computes the ranking induced + by degrees, where the node with the highest degree will be assigned a + rank equal to \textbf{1} (one). +} + +\myreturn{The program prints on \texttt{stdout} a list of lines, where + the n-th line contains the rank of the n-th node corresponding to the + values of the structural descriptor provided in the input file.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/correlations/rank_nodes_thresh.tex b/doc/latex/latex/structure/correlations/rank_nodes_thresh.tex new file mode 100644 index 0000000..3b430d1 --- /dev/null +++ b/doc/latex/latex/structure/correlations/rank_nodes_thresh.tex @@ -0,0 +1,18 @@ +\myprogram{{rank\_nodes\_thresh.py}} + {rank the nodes of a layer whose value of a given structural + descriptor is above a threshold.} {$<$prop\_file$>$ $<$thresh$>$} + +\mydescription{Get a file as input, whose n-th line corresponds to the value of a + certain property of the n-th node, and rank the nodes according to + that property, taking into account ranking ties properly. The rank of + all the nodes whose value of the structural descriptor is smaller + than the threshold \textit{thresh} specified as second parameter is + set to \textbf{0} (ZERO). } + +\myreturn{The program prints on \texttt{stdout} a list of lines, where + the n-th line contains the rank of the n-th node corresponding to the + values of the structural descriptor provided in the input file, or + zero if such desxriptor is below the specified + threshold \textit{thresh}.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/correlations/rank_occurrence.tex b/doc/latex/latex/structure/correlations/rank_occurrence.tex new file mode 100644 index 0000000..96fb914 --- /dev/null +++ b/doc/latex/latex/structure/correlations/rank_occurrence.tex @@ -0,0 +1,24 @@ +\myprogram{{rank\_occurrence.py}} + {compute the intersection of two rankings.} + {$<$rank1$>$ $<$rank2$>$ $<$increment$>$} + +\mydescription{Get two rankings \textit{rank1} and \textit{rank2} + and compute the size of +the \textit{k}-intersection, i.e. the number of elements which are +present in the first k positions of both rankings, as a function +of \textit{k}. The parameter \textit{increment} determines the +distance between two subsequent values of \textit{k}. + +Each input file is a list of node IDs, one per line, where the first +line contains the ID of the highest ranked node. +} + +\myreturn{The program prints on \texttt{stdout} a list of lines in the +format: + + \hspace{0.5cm} \textit{k num\_k} + + where \textit{num\_k} is the number of nodes which are present in + the first \textit{k} positions of both rankings.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/metrics/aggregate_layers_w.tex b/doc/latex/latex/structure/metrics/aggregate_layers_w.tex new file mode 100644 index 0000000..8917e3e --- /dev/null +++ b/doc/latex/latex/structure/metrics/aggregate_layers_w.tex @@ -0,0 +1,30 @@ +\myprogram{{aggregate\_layers\_w.py}} + {compute the (weighted) aggregated graph associated to a + multiplex.} {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]} + +\mydescription{Compute and print on output the edge list of the + weighted aggregated graph associated to the multiplex + network given on input. An edge is present in the + aggregated graph if it exists in at least one of the M + layers of the multiplex. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} the edge list of the + aggregated graph associated to the multiplex network. The edge list + is a list of lines in the format: + + + \hspace{0.5cm} \textit{ID1 ID2 weight} + + \noindent where \textit{ID1} and \textit{ID2} are the IDs of the two + nodes and \textit{weight} is the number of layers in which an edge + between \textit{ID1} and \textit{ID2} exists.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/metrics/avg_edge_overlap.tex b/doc/latex/latex/structure/metrics/avg_edge_overlap.tex new file mode 100644 index 0000000..4df2d51 --- /dev/null +++ b/doc/latex/latex/structure/metrics/avg_edge_overlap.tex @@ -0,0 +1,42 @@ +\myprogram{{avg\_edge\_overlap.py}} + {compute the average edge overlap of a multiplex.} + {$<$layer1$>$ [$<$layer2$>$...]} + +\mydescription{Compute and print on output the average edge overlap + + \begin{equation*} \omega^{*} + = \frac{\sum_{i}\sum_{j>i}\sum_{\alpha}a_{ij}\lay{\alpha}}{ \sum_{i}\sum_{j>i}(1 + - \delta_{0,\sum_{\alpha}a_{ij}\lay{\alpha}})} \end{equation*} + + \noindent i.e., the expected \textit{number} of layers on which an + edge of the multiplex exists, and the corresponding normalised + quantity: + + \begin{equation*} + \omega = \frac{\sum_{i}\sum_{j>i}\sum_{\alpha}a_{ij}\lay{\alpha}}{M \sum_{i}\sum_{j>i}(1 + - \delta_{0,\sum_{\alpha}a_{ij}\lay{\alpha}})} + \end{equation*} + + \noindent that is the expected \textit{fraction} of layers on which + an edge of the multiplex is present. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a single line, in the + format: + + \hspace{0.5cm} \textit{omega\_star omega} + + \noindent where \textit{omega\_star} and \textit{omega} are, + respectively, the expected number and fraction of layers in which an + edge is present.} + +\myreference{\refmetrics + + \vspace{0.5cm}\refvisibility} diff --git a/doc/latex/latex/structure/metrics/cartography_from_columns.tex b/doc/latex/latex/structure/metrics/cartography_from_columns.tex new file mode 100644 index 0000000..8e797af --- /dev/null +++ b/doc/latex/latex/structure/metrics/cartography_from_columns.tex @@ -0,0 +1,35 @@ +\myprogram{{cartography\_from\_columns.py}} + {compute total and participation coefficient of generic + structural descriptors of the nodes of a multiplex.} + {$<$filein$>$ $<$col1$>$ $<$col2$>$ [$<$col3$>$...]} + +\mydescription{Compute and print on output the sum and the + corresponding participation coefficient of a generic + structural descriptor of the nodes of a multiplex. + + \noindent The input file is a generic collection of + single-space-separated columns, where each line corresponds to a + node. The user must specify the IDs of the columns which contain + the node structural descriptors to be used in the cartography + diagram. Columns IDs start from ZERO. For example: + + \textbf{python cartography\_from\_layers.py filein.txt 0 + 2 4 6 8} + + \noindent will create a cartography diagram assuming that the + multiplex network has five layers, and that the node structural + descriptors at each layers are contained in the first (0), third + (2), fifth (4), seventh (6) and nineth (8) columns of each row.} + + +\myreturn{The program prints on \texttt{stdout} a list of lines in the + format: + + \hspace{0.5cm} \textit{tot\_n P\_n} + + where \textit{tot\_n} is the sum over the layers of the considered + structural descriptor for node $n$, and \textit{P\_n} is the + associated participation coefficient + } + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/metrics/cartography_from_deg_vectors.tex b/doc/latex/latex/structure/metrics/cartography_from_deg_vectors.tex new file mode 100644 index 0000000..848ffd1 --- /dev/null +++ b/doc/latex/latex/structure/metrics/cartography_from_deg_vectors.tex @@ -0,0 +1,32 @@ +\myprogram{{cartography\_from\_deg\_vectors.py}} + {create a multiplex cartography diagram.} + {$<$node\_deg\_vectors$>$} + +\mydescription{Compute and print on output the total degree and the + multiplex participation coefficient of all the nodes of a + multiplex network whose list of node degree vectors is + provided as input. The input file is in the format: + + \hspace{0.5cm} \textit{IDn\_deg1 IDn\_deg\_2 ... IDn\_degM} + + \noindent where \textit{IDn\_degX} is the degree of node $n$ at + layer $X$. The input file can be generated using the + script \texttt{node\_degree\_vectors.py}.} + + +\myreturn{The program prints on \texttt{stdout} a list of lines in the + format: + + \hspace{0.5cm} \textit{tot\_deg part\_coeff} + + \noindent where \textit{tot\_deg} is the total degree of the node + and \textit{part\_coeff} is the corresponding participation + coefficient. + + \noindent As usual, node IDs start from zero and proceed + sequentially, without gaps, so if one of the lines in the input + files contains just zeros, the program considers the corresponding + node as being isolated on all the layers, and both its total degree + and multiplex participation coefficient are set equal to zero. } + +\myreference{\refmetrics} diff --git a/doc/latex/latex/structure/metrics/cartography_from_layers.tex b/doc/latex/latex/structure/metrics/cartography_from_layers.tex new file mode 100644 index 0000000..8958cef --- /dev/null +++ b/doc/latex/latex/structure/metrics/cartography_from_layers.tex @@ -0,0 +1,45 @@ +\myprogram{{cartography\_from\_layers.py}} + {compute the total degree and the multiplex participation + coefficient of all the nodes of a multiplex.} {$<$layer1$>$ + $<$layer2$>$ [$<$layer3$>$...]} + +\mydescription{Compute and print on output the total degree and the multiplex participation + coefficient $P_i$ for each node $i$ of a multiplex. The + participation coefficient is defined as: + + \begin{equation*} + P_i=\frac{M}{M-1}\left[1-\sum_{\alpha=1}^M\biggl(\frac{k_i^{[\alpha]}}{o_i}\biggr)^2\right] + \end{equation*} + + \noindent Note that $P_i$ takes values in $[0,1]$, where $P_i=0$ + if and only if node $i$ is active on exactly one of the layers, + while $P_i=1$ if node $i$ has equal degree on all the $M$ layers. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines in the + format: + + \hspace{0.5cm} \textit{deg\_n P\_n col\_n} + + where \textit{deg\_n} is the total degree of node $n$, \textit{P\_n} + is the participation coefficient of node $n$ and \textit{col} is the + integer representation of the activity bitstring of node $n$, which + is a number between $0$ and $2^{M}-1$. The field \textit{col} might + be useful for the visualisation of the multiplex cartography + diagram, where it would be possible to associate different colors to + nodes having different node activity patterns. + + \noindent As usual, node IDs start from zero and proceed + sequentially, without gaps, i.e., if a node ID is not present in any + of the layer files given as input, the program considers it as being + isolated on all the layers, and is set to zero. + } + +\myreference{\refmetrics} diff --git a/doc/latex/latex/structure/metrics/edge_overlap.tex b/doc/latex/latex/structure/metrics/edge_overlap.tex new file mode 100644 index 0000000..64d7dbf --- /dev/null +++ b/doc/latex/latex/structure/metrics/edge_overlap.tex @@ -0,0 +1,36 @@ +\myprogram{{edge\_overlap.py}} + {compute the edge overlap of all the edges of the + multiplex.} + {$<$layer1$>$ [$<$layer2$>$...]} + +\mydescription{Compute and print on output the edge overlap $o_{ij}$ of each + edge of the multiplex. Given a pair of nodes $(i,j)$ that + are directly connected on at least one of the $M$ layers, + the edge overlap $o_{ij}$ is defined as: + + \begin{equation*} + o_{ij} = \sum_{\alpha}a_{ij}\lay{\alpha} + \end{equation*} + + \noindent i.e., the number of layers on which the edge $(i,j)$ + exists. + + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines in the + format: + + \hspace{0.5cm} \textit{ID\_1 ID\_2 overlap} + + \noindent where \textit{ID\_1} and \textit{ID\_2} are the IDs of the + end-points of the edge, and \textit{overlap} is the number of layers + in which the edge exists.} + +\myreference{\refmetrics} diff --git a/doc/latex/latex/structure/metrics/intersect_layers.tex b/doc/latex/latex/structure/metrics/intersect_layers.tex new file mode 100644 index 0000000..0824400 --- /dev/null +++ b/doc/latex/latex/structure/metrics/intersect_layers.tex @@ -0,0 +1,28 @@ +\myprogram{{intersect\_layers.py}} + {compute the intersection graph associated to a + multiplex.} {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]} + +\mydescription{Compute and print on output the edge list of the + intersection graph associated to the multiplex network + given on input, where an edge exists only if it is + present on \textbf{all} the layers of the multiplex. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} the edge list of the + intersection graph associated to the multiplex network. The edge + list is a list of lines in the format: + + + \hspace{0.5cm} \textit{ID1 ID2} + + \noindent where \textit{ID1} and \textit{ID2} are the IDs of the two + nodes.} + +\myreference{\refcorrelations} diff --git a/doc/latex/latex/structure/metrics/overlap_degree.tex b/doc/latex/latex/structure/metrics/overlap_degree.tex new file mode 100644 index 0000000..500a76a --- /dev/null +++ b/doc/latex/latex/structure/metrics/overlap_degree.tex @@ -0,0 +1,45 @@ +\myprogram{{overlap\_degree.py}} + {compute the total (overlapping) degree of all the nodes of + a multiplex and the corresponding Z-score. } {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]} + +\mydescription{Compute and print on output the total degree $o_i$ of each + node $i$ of a multiplex, defined as: + + \begin{equation*} + o_{i} = \sum_{\alpha}\sum_{j}a_{ij}\lay{\alpha} + \end{equation*} + + \noindent and the corresponding Z-score: + + \begin{equation*} + z(o_i) = \frac{o_i - \avg{o}}{\sigma_o} + \end{equation*} + + \noindent where $\avg{o}$ and $\sigma_o$ are, respectively, the mean + and the standard deviation of the total degree computed over all the + active nodes of the multiplex. + + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines in the + format: + + \hspace{0.5cm} \textit{ID\_n deg\_n z\_n} + + where \textit{ID\_n} is the ID of the node, \textit{deg\_n} is its + total degree, and \textit{z\_n} is the corresponding Z-score. + + \noindent As usual, node IDs start from zero and proceed + sequentially, without gaps, i.e., if a node ID is not present in any + of the layer files given as input, the program considers it as being + isolated on all the layers, and the node is omitted from the + output.} + +\myreference{\refmetrics} diff --git a/doc/latex/latex/structure/metrics/part_coeff.tex b/doc/latex/latex/structure/metrics/part_coeff.tex new file mode 100644 index 0000000..f3afd7d --- /dev/null +++ b/doc/latex/latex/structure/metrics/part_coeff.tex @@ -0,0 +1,43 @@ +\myprogram{{part\_coeff.py}} + {compute the multiplex partifipation coefficient of all the nodes of + a multiplex.} {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]} + +\mydescription{Compute and print on output the multiplex participation + coefficient $P_i$ for each node $i$ of a multiplex. The + participation coefficient is defined as: + + \begin{equation*} + P_i=\frac{M}{M-1}\left[1-\sum_{\alpha=1}^M\biggl(\frac{k_i^{[\alpha]}}{o_i}\biggr)^2\right] + \end{equation*} + + \noindent Note that $P_i$ takes values in $[0,1]$, where $P_i=0$ + if and only if node $i$ is active on exactly one of the layers, + while $P_i=1$ if node $i$ has equal degree on all the $M$ layers. + + Each input file contains the (undirected) edge list of a layer, and + each line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge.} + +\myreturn{The program prints on \texttt{stdout} a list of lines in the + format: + + \hspace{0.5cm} \textit{deg\_n P\_n col\_n} + + where \textit{deg\_n} is the total degree of node $n$, \textit{P\_n} + is the participation coefficient of node $n$ and \textit{col} is the + integer representation of the activity bitstring of node $n$, which + is a number between $0$ and $2^{M}-1$. The field \textit{col} might + be useful in visualisations, where it would be possible to associate + different colors to nodes having diffrent node activity patterns. + + \noindent As usual, node IDs start from zero and proceed + sequentially, without gaps, i.e., if a node ID is not present in any + of the layer files given as input, the program considers it as being + isolated on all the layers, and is set to zero. + } + +\myreference{\refmetrics} diff --git a/doc/latex/latex/structure/reinforcement/reinforcement.tex b/doc/latex/latex/structure/reinforcement/reinforcement.tex new file mode 100644 index 0000000..a65b05e --- /dev/null +++ b/doc/latex/latex/structure/reinforcement/reinforcement.tex @@ -0,0 +1,21 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{reinforcement.py}} + {compute the probability to have a link between two nodes in layer $1$ given their weight in layer $2$.} + {$<$layer1$>$ $<$layer2$>$ $<N_{bins}>$ $<min_{value}>$ $<max_{value}>$} + +\mydescription{Compute and print on output the probability to have a link between two nodes in layer $1$ given their weight in layer $2$. +As input are given the files \textit{layer1}, \textit{layer2}, the number of bins for the link weights of the second layer, the minimum and the maximum values of the binning. + + The first file contains the binary edge list of layer $1$, the second file contains the weighted edge list of layer $2$. each + line is in the format: + + \hspace{0.5cm}\textit{bin\_min} \textit{bin\_max} \textit{freq} + + where \textit{bin\_min} and \textit{bin\_max} are the minimum and maximum values of the link weights of layer $2$ in that binning, and \textit{freq} is the probability to have a link on layer $1$ given such weight in layer $2$.} + +\myreturn{A list of lines, where the n-th line is the minimum and maximum values of the weight of the links in layer $2$ in the n-th bin, and the frequency to have a link on layer $2$ given that weight.} + +\myreference{\refmetrics} diff --git a/doc/latex/mammult_doc.tex b/doc/latex/mammult_doc.tex new file mode 100644 index 0000000..4d93d88 --- /dev/null +++ b/doc/latex/mammult_doc.tex @@ -0,0 +1,265 @@ +\documentclass[a4paper,11pt]{book} + +\usepackage[british]{babel} +\usepackage[latin1]{inputenc} +\usepackage{hyperref} +\usepackage{amsmath, amssymb} + +\newcommand{\lay}[1]{^{[#1]}} +\newcommand{\avg}[1]{\langle #1 \rangle} + + +\newcommand{\myprogram}[3]{\subsubsection{\texttt{#1}} + \textbf{NAME} + + {\textbf{#1} - #2} + + \vspace{0.5cm} + \noindent + \textbf{SYNOPSYS} + + {\textbf{#1} { }\texttt{\textit{#3} } } +} + +\newcommand{\mydescription}[1]{ + \vspace{0.5cm} + \noindent + \textbf{DESCRIPTION} + + {#1} +} + +\newcommand{\myreturn}[1]{ + \vspace{0.5cm} + \noindent + \textbf{OUTPUT} + + {#1} +} + + +\newcommand{\myreference}[1]{ + \vspace{0.5cm} + \noindent + \textbf{REFERENCE} + + {#1} +} + +%% +%% REFERENCES +%% + +\newcommand{\refgrowth}{V. Nicosia, G. Bianconi, V. Latora, + M. Barthelemy, ``Growing multiplex networks'', + \textit{Phys. Rev. Lett.} {\bf 111}, 058701 (2013). + + Link to paper: \url{http://prl.aps.org/abstract/PRL/v111/i5/e058701} +} +\newcommand{\refnonlinear}{V. Nicosia, G. Bianconi, V. Latora, + M. Barthelemy, ``Non-linear growth and condensation in multiplex + networks'', \textit{Phys. Rev. E} {\bf 90}, 042807 (2014). + + Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807} +} +\newcommand{\refmetrics}{F. Battiston, V. Nicosia, V. Latora, + ``Structural measures for multiplex networks'', + \textit{Phys. Rev. E} {\bf 89}, 032804 (2014). + + Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804} +} +\newcommand{\refcorrelations}{V. Nicosia, V. Latora, ``Measuring and + modeling correlations in multiplex networks'', \textit{Phys. Rev. E} + {\bf 92}, 032805 (2015). + + Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805}} + +\newcommand{\refreducibility}{M. De Domenico, V. Nicosia, A. Arenas, + V. Latora, \textit{``Structural reducibility of multilayer + networks''}, Nat. Commun. {\bf 6}, 6864 (2015). + + Link to paper: \url{http://www.nature.com/ncomms/2015/150423/ncomms7864/full/ncomms7864.html} +} +\newcommand{\refvisibility}{L. Lacasa, V. Nicosia, V. Latora, + \textit{``Network structure of multivariate time series''}, accepted + for publication in Scientific Reports, arxiv:1408.0925 (2015). + + Link to paper: \url{http://arxiv.org/abs/1408.0925} +} + +\newcommand{\refbiased}{F. Battiston, V. Nicosia, V. Latora, + \textit{``Biased random walks on multiplex networks''}, arxiv:1505.01378 (2015). + + Link to paper: \url{http://arxiv.org/abs/1505.01378} +} +\newcommand{\refising}{F. Battiston, A. Cairoli, V. Nicosia, A. Baule, V. Latora, + \textit{``Interplay between consensus and coherence in a model of interacting opinions''}, accepted + for publication in Physica D, arxiv:1506.04544 (2015). + + Link to paper: \url{http://arxiv.org/abs/1506.04544} +} +\newcommand{\refcommunity}{F. Battiston, J. Iacovacci, V. Nicosia, G. Bianconi, V. Latora, + \textit{``Emergence of multiplex communities in collaboration networks''}, arxiv:1506.01280 (2015). + + Link to paper: \url{http://arxiv.org/abs/1506.01280} +} + +\newcommand{\refaxelrod}{F. Battiston, V. Nicosia, V. Latora, M. San Miguel, + \textit{``Layered social influence promotes multiculturality''}, in preparation (2015). + + %Link to paper: \url{http://arxiv.org/abs/inpreparation} +} +\newcommand{\refmotifs}{F. Battiston, M. Chavez, V. Nicosia, V. Latora, + \textit{``Multilayer motifs in brain networks''}, in preparation (2015). + + %Link to paper: \url{http://arxiv.org/abs/inpreparation} +} + +\title{MAMMULT: Metrics And Models for MULTilayer networks} + + +\begin{document} + +\maketitle + +\chapter{Structural descriptors} + +\section{Basic node, edge, and layer properties} + +\subsection{Node and layer activity} + +This section includes programs related to the computation of node and +layer activity, activity vectors, pairwise multiplexity, pairwise +normalised Hamming distance, node degree vectors. + +\input{./latex/structure/activity/node_activity.tex} +\input{./latex/structure/activity/layer_activity.tex} +\input{./latex/structure/activity/node_activity_vectors.tex} +\input{./latex/structure/activity/layer_activity_vectors.tex} +\input{./latex/structure/activity/multiplexity.tex} +\input{./latex/structure/activity/hamming_dist.tex} +\input{./latex/structure/activity/node_degree_vectors.tex} +\input{./latex/structure/activity/degs_to_binary.tex} +\input{./latex/structure/activity/degs_to_activity_overlap.tex} + +\subsection{Layer aggregation} + +This section includes programs to obtain various single-layer +aggregated graphs associated to a multiplex network. + +\input{./latex/structure/metrics/aggregate_layers_w.tex} +\input{./latex/structure/metrics/intersect_layers.tex} + +\subsection{Node degree, participation coefficient, cartography} + +This section includes programs to compute the total degree and +participation coefficient of each node, and to draw the cartography +diagram of a multiplex. + +\input{./latex/structure/metrics/overlap_degree.tex} +\input{./latex/structure/metrics/cartography_from_layers.tex} +\input{./latex/structure/metrics/cartography_from_deg_vectors.tex} +\input{./latex/structure/metrics/cartography_from_columns.tex} + +\subsection{Edge overlap, reinforcement} +This section includes programs to compute the egde overlap and to +evaulate the edge reinforcement effect. + +\input{./latex/structure/metrics/edge_overlap.tex} +\input{./latex/structure/metrics/avg_edge_overlap.tex} +\input{./latex/structure/reinforcement/reinforcement.tex} + +\section{Inter-layer degree correlations} + +\subsection{Node ranking} + +This section includes various utilities to compute and compare node +rankings induced by any generic structural node property, including +degree at different layers. + +\input{./latex/structure/correlations/rank_nodes.tex} +\input{./latex/structure/correlations/rank_nodes_thresh.tex} +\input{./latex/structure/correlations/rank_occurrence.tex} + +\subsection{Interlayer degree correlation coefficients} + +This section includes programs for the computation of various +inter-layer degree correlation coefficients. + +\input{./latex/structure/correlations/compute_pearson.tex} +\input{./latex/structure/correlations/compute_rho.tex} +\input{./latex/structure/correlations/compute_tau.tex} + + +\subsection{Interlayer degree correlation functions} + +This section includes programs to compute intra-layer and inter-layer +degree correlation functions, and to fit those functions with a +power-law. + + +\input{./latex/structure/correlations/dump_k_q.tex} +\input{./latex/structure/correlations/knn_q_from_layers.tex} +%% \input{./latex/structure/correlations/knn_q_from_layers_log.tex} +\input{./latex/structure/correlations/knn_q_from_degrees.tex} +%% \input{./latex/structure/correlations/knn_q_from_degrees_log.tex} +\input{./latex/structure/correlations/fit_knn.tex} + +\chapter{Models of multi-layer networks} + +\section{Null models} + +\subsection{Null-models of node and layer activity} + +\input{./latex/models/nullmodels/model_hypergeometric.tex} +\input{./latex/models/nullmodels/model_MDM.tex} +\input{./latex/models/nullmodels/model_MSM.tex} +\input{./latex/models/nullmodels/model_layer_growth.tex} + + +\section{Growing multiplex networks} + +\subsection{Linear preferential attachment} + +\input{./latex/models/growth/nibilab_linear_delta.tex} +\input{./latex/models/growth/nibilab_linear_delay.tex} +\input{./latex/models/growth/nibilab_linear_delay_mix.tex} +\input{./latex/models/growth/nibilab_linear_random_times.tex} +%%\input{./latex/models/growth/nibilab_semilinear.tex} + +\subsection{Non-linear preferential attachment} + +\input{./latex/models/growth/nibilab_nonlinear.tex} + + +\subsection{Utilities} + +\input{./latex/models/growth/node_deg_over_time.tex} + +\section{Multiplex networks with inter-layer degree correlations} + +\subsection{Models based on simulated annealing} + +\input{./latex/models/correlations/tune_rho.tex} +\input{./latex/models/correlations/tune_qnn_adaptive.tex} + + +\chapter{Dynamics on multi-layer networks} + +\section{Interacting opinions - Multilayer ising model} + +\input{./latex/dynamics/Ising/multiplex_ising.tex} + +\section{Biased random walks} + +\subsection{Stationary distribution} + +\input{./latex/dynamics/randomwalks/statdistr2.tex} + +\subsection{Entropy rate} + +\input{./latex/dynamics/randomwalks/entropyrate2add.tex} +\input{./latex/dynamics/randomwalks/entropyrate2mult.tex} +\input{./latex/dynamics/randomwalks/entropyrate2int.tex} + +\end{document} |
