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| author | KatolaZ <katolaz@yahoo.it> | 2015-10-19 16:30:12 +0100 |
|---|---|---|
| committer | KatolaZ <katolaz@yahoo.it> | 2015-10-19 16:30:12 +0100 |
| commit | a86962cbfd0321387c920a04188512d0de2f3036 (patch) | |
| tree | b6c0d31342f7af9d605ee83cfffe251554a307d4 /doc/html/mammult_docsu44.html | |
| parent | df8386f75b0538075d72d52693836bb8878f505b (diff) | |
First commit of MAMMULT documentation
Diffstat (limited to 'doc/html/mammult_docsu44.html')
| -rw-r--r-- | doc/html/mammult_docsu44.html | 163 |
1 files changed, 163 insertions, 0 deletions
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> |