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authorKatolaZ <katolaz@freaknet.org>2017-09-27 15:06:31 +0100
committerKatolaZ <katolaz@freaknet.org>2017-09-27 15:06:31 +0100
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+<!DOCTYPE html>
+<html>
+<head>
+ <meta http-equiv='content-type' value='text/html;charset=utf8'>
+ <meta name='generator' value='Ronn/v0.7.3 (http://github.com/rtomayko/ronn/tree/0.7.3)'>
+ <title>pm(1) - Compute the leading eigenvalue and eigenvector of a graph</title>
+ <style type='text/css' media='all'>
+ /* style: man */
+ body#manpage {margin:0}
+ .mp {max-width:100ex;padding:0 9ex 1ex 4ex}
+ .mp p,.mp pre,.mp ul,.mp ol,.mp dl {margin:0 0 20px 0}
+ .mp h2 {margin:10px 0 0 0}
+ .mp > p,.mp > pre,.mp > ul,.mp > ol,.mp > dl {margin-left:8ex}
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+ .mp dt {margin:0;clear:left}
+ .mp dt.flush {float:left;width:8ex}
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+ .mp img {display:block;margin:auto}
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+ .mp,.mp code,.mp pre,.mp tt,.mp kbd,.mp samp,.mp h3,.mp h4 {font-family:monospace;font-size:14px;line-height:1.42857142857143}
+ .mp h2 {font-size:16px;line-height:1.25}
+ .mp h1 {font-size:20px;line-height:2}
+ .mp {text-align:justify;background:#fff}
+ .mp,.mp code,.mp pre,.mp pre code,.mp tt,.mp kbd,.mp samp {color:#131211}
+ .mp h1,.mp h2,.mp h3,.mp h4 {color:#030201}
+ .mp u {text-decoration:underline}
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+ ol.man-decor,ol.man-decor li {margin:3px 0 10px 0;padding:0;float:left;width:33%;list-style-type:none;text-transform:uppercase;color:#999;letter-spacing:1px}
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+ ol.man-decor li.tc {text-align:center;letter-spacing:4px}
+ ol.man-decor li.tr {text-align:right;float:right}
+ </style>
+ <style type='text/css' media='all'>
+ /* style: toc */
+ .man-navigation {display:block !important;position:fixed;top:0;left:113ex;height:100%;width:100%;padding:48px 0 0 0;border-left:1px solid #dbdbdb;background:#eee}
+ .man-navigation a,.man-navigation a:hover,.man-navigation a:link,.man-navigation a:visited {display:block;margin:0;padding:5px 2px 5px 30px;color:#999;text-decoration:none}
+ .man-navigation a:hover {color:#111;text-decoration:underline}
+ </style>
+</head>
+<!--
+ The following styles are deprecated and will be removed at some point:
+ div#man, div#man ol.man, div#man ol.head, div#man ol.man.
+
+ The .man-page, .man-decor, .man-head, .man-foot, .man-title, and
+ .man-navigation should be used instead.
+-->
+<body id='manpage'>
+ <div class='mp' id='man'>
+
+ <div class='man-navigation' style='display:none'>
+ <a href="#NAME">NAME</a>
+ <a href="#SYNOPSIS">SYNOPSIS</a>
+ <a href="#DESCRIPTION">DESCRIPTION</a>
+ <a href="#PARAMETERS">PARAMETERS</a>
+ <a href="#EXAMPLES">EXAMPLES</a>
+ <a href="#REFERENCES">REFERENCES</a>
+ <a href="#AUTHORS">AUTHORS</a>
+ </div>
+
+ <ol class='man-decor man-head man head'>
+ <li class='tl'>pm(1)</li>
+ <li class='tc'>www.complex-networks.net</li>
+ <li class='tr'>pm(1)</li>
+ </ol>
+
+ <h2 id="NAME">NAME</h2>
+<p class="man-name">
+ <code>pm</code> - <span class="man-whatis">Compute the leading eigenvalue and eigenvector of a graph</span>
+</p>
+
+<h2 id="SYNOPSIS">SYNOPSIS</h2>
+
+<p><code>pm</code> <var>graph_in</var> <var>is_dir</var> <var>eps</var></p>
+
+<h2 id="DESCRIPTION">DESCRIPTION</h2>
+
+<p><code>pm</code> computes the leading eigenvalue and the corresponding eigenvector
+of the matrix given as input, using the Power Method. In particular,
+this implementation uses the Rayleigh iteration, which allows faster
+convergence on undirected graphs.</p>
+
+<h2 id="PARAMETERS">PARAMETERS</h2>
+
+<dl>
+<dt><var>graph_in</var></dt><dd><p> input graph (edge list) if equal to <code>-</code> (dash), read the edge list
+ from STDIN (standard input).</p></dd>
+<dt class="flush"><var>is_dir</var></dt><dd><p> set either to <code>0</code> (zero) for undirected graphs, or to <code>1</code> (one)
+ for directed graphs.</p></dd>
+<dt class="flush"><var>eps</var></dt><dd><p> Required relative error on the approximation of the leading
+ eigenvalue. The program terminates when the relative change in the
+ approximation of the eigenvalue is smaller than <code>eps</code></p></dd>
+</dl>
+
+
+<h2 id="EXAMPLES">EXAMPLES</h2>
+
+<p>The following command:</p>
+
+<pre><code> $ pm er_1000_5000.net 0 0.0000001
+</code></pre>
+
+<p>computes the leading eigenvalue and the corresponding eigenvector of
+the undirected graph stored in the file <code>er_1000_5000.txt</code>. We can
+store the leading eigenvector in a file, e.g. by using the command:</p>
+
+<pre><code> $ pm er_1000_5000.net 0 0.0000001 &gt; er_1000_5000.net_eig
+ 11.0335794552533
+ $
+</code></pre>
+
+<p>which will save the leading eigenvector in the file
+<code>er_1000_5000.net_eig</code>, one component for each row, and shown on
+output the leading eigenvalue of the graph.</p>
+
+<h2 id="REFERENCES">REFERENCES</h2>
+
+<ul>
+<li>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Appendix 5, Cambridge University Press
+(2017)</li>
+</ul>
+
+
+<h2 id="AUTHORS">AUTHORS</h2>
+
+<p>(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <code>&lt;v.nicosia@qmul.ac.uk&gt;</code>.</p>
+
+
+ <ol class='man-decor man-foot man foot'>
+ <li class='tl'>www.complex-networks.net</li>
+ <li class='tc'>September 2017</li>
+ <li class='tr'>pm(1)</li>
+ </ol>
+
+ </div>
+</body>
+</html>
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