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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> |