From a86962cbfd0321387c920a04188512d0de2f3036 Mon Sep 17 00:00:00 2001 From: KatolaZ <katolaz@yahoo.it> Date: Mon, 19 Oct 2015 16:30:12 +0100 Subject: First commit of MAMMULT documentation --- doc/html/mammult_docsu45.html | 146 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 146 insertions(+) create mode 100644 doc/html/mammult_docsu45.html (limited to 'doc/html/mammult_docsu45.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> -- cgit v1.2.3