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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> |
