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diff --git a/doc/dms.1.html b/doc/dms.1.html new file mode 100644 index 0000000..e51aa79 --- /dev/null +++ b/doc/dms.1.html @@ -0,0 +1,183 @@ +<!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>dms(1) - Grow a scale-free random graph with tunable exponent</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} + .mp h3 {margin:0 0 0 4ex} + .mp dt {margin:0;clear:left} + .mp dt.flush {float:left;width:8ex} + .mp dd {margin:0 0 0 9ex} + .mp h1,.mp h2,.mp h3,.mp h4 {clear:left} + .mp pre {margin-bottom:20px} + .mp pre+h2,.mp pre+h3 {margin-top:22px} + .mp h2+pre,.mp h3+pre {margin-top:5px} + .mp img {display:block;margin:auto} + .mp h1.man-title {display:none} + .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} + .mp code,.mp strong,.mp b {font-weight:bold;color:#131211} + .mp em,.mp var {font-style:italic;color:#232221;text-decoration:none} + .mp a,.mp a:link,.mp a:hover,.mp a code,.mp a pre,.mp a tt,.mp a kbd,.mp a samp {color:#0000ff} + .mp b.man-ref {font-weight:normal;color:#434241} + .mp pre {padding:0 4ex} + .mp pre code {font-weight:normal;color:#434241} + .mp h2+pre,h3+pre {padding-left:0} + 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} + ol.man-decor {width:100%} + ol.man-decor li.tl {text-align:left} + 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="#OUTPUT">OUTPUT</a> + <a href="#EXAMPLES">EXAMPLES</a> + <a href="#SEE-ALSO">SEE ALSO</a> + <a href="#REFERENCES">REFERENCES</a> + <a href="#AUTHORS">AUTHORS</a> + </div> + + <ol class='man-decor man-head man head'> + <li class='tl'>dms(1)</li> + <li class='tc'>www.complex-networks.net</li> + <li class='tr'>dms(1)</li> + </ol> + + <h2 id="NAME">NAME</h2> +<p class="man-name"> + <code>dms</code> - <span class="man-whatis">Grow a scale-free random graph with tunable exponent</span> +</p> + +<h2 id="SYNOPSIS">SYNOPSIS</h2> + +<p><code>dms</code> <var>N</var> <var>m</var> <var>n0</var> <em>a</em></p> + +<h2 id="DESCRIPTION">DESCRIPTION</h2> + +<p><code>dms</code> grows an undirected random scale-free graph with <var>N</var> nodes using +the modified linear preferential attachment model proposed by +Dorogovtsev, Mendes and Samukhin. The initial network is a clique of +<var>n0</var> nodes, and each new node creates <var>m</var> new edges. The resulting +graph will have a scale-free degree distribution, whose exponent +converges to <code>gamma=3.0 + a/m</code> for large <var>N</var>.</p> + +<h2 id="PARAMETERS">PARAMETERS</h2> + +<dl> +<dt class="flush"><var>N</var></dt><dd><p> Number of nodes of the final graph.</p></dd> +<dt class="flush"><var>m</var></dt><dd><p> Number of edges created by each new node.</p></dd> +<dt class="flush"><var>n0</var></dt><dd><p> Number of nodes in the initial (seed) graph.</p></dd> +<dt class="flush"><em>a</em></dt><dd><p> This parameter sets the exponent of the degree distribution + (<code>gamma = 3.0 + a/m</code>). <em>a</em> must be larger than <var>-m</var>.</p></dd> +</dl> + + +<h2 id="OUTPUT">OUTPUT</h2> + +<p><code>dms</code> prints on STDOUT the edge list of the final graph.</p> + +<h2 id="EXAMPLES">EXAMPLES</h2> + +<p>Let us assume that we want to create a scale-free network with +<var>N=10000</var> nodes, with average degree equal to 8, whose degree +distribution has exponent</p> + +<pre><code> gamma = 2.5 +</code></pre> + +<p>Since <code>dms</code> produces graphs with scale-free degree sequences with an +exponent <code>gamma = 3.0 + a/m</code>, the command:</p> + +<pre><code> $ dms 10000 4 4 -2.0 > dms_10000_4_4_-2.0.txt +</code></pre> + +<p>will produce the desired network. In fact, the average degree of the +graph will be:</p> + +<pre><code> <k> = 2m = 8 +</code></pre> + +<p>and the exponent of the power-law degree distribution will be:</p> + +<pre><code> gamma = 3.0 + a/m = 3.0 -0.5 = 2.5 +</code></pre> + +<p>The following command:</p> + +<pre><code> $ dms 10000 3 5 0 > dms_10000_3_5_0.txt +</code></pre> + +<p>creates a scale-free graph with <var>N=10000</var> nodes, where each new node +creates <var>m=3</var> new edges and the initial seed network is a ring of +<var>n0=5</var> nodes. The degree distribution of the final graph will have +exponent equal to <code>gamma = 3.0 + a/m = 3.0</code>. In this case, <code>dms</code> +produces a Barabasi-Albert graph (see <a class="man-ref" href="ba.1.html">ba<span class="s">(1)</span></a> for details). The edge +list of the graph is saved in the file <code>dms_10000_3_5_0.txt</code> (thanks +to the redirection operator <code>></code>).</p> + +<h2 id="SEE-ALSO">SEE ALSO</h2> + +<p><a class="man-ref" href="ba.1.html">ba<span class="s">(1)</span></a>, <a class="man-ref" href="bb_fitness.1.html">bb_fitness<span class="s">(1)</span></a></p> + +<h2 id="REFERENCES">REFERENCES</h2> + +<ul> +<li><p>S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin. "Structure of + Growing Networks with Preferential Linking". Phys. Rev. Lett. 85 + (2000), 4633-4636.</p></li> +<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, +Methods and Applications", Chapter 6, Cambridge University Press +(2017)</p></li> +<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, +Methods and Applications", Appendix 13, Cambridge University Press +(2017)</p></li> +</ul> + + +<h2 id="AUTHORS">AUTHORS</h2> + +<p>(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <code><v.nicosia@qmul.ac.uk></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'>dms(1)</li> + </ol> + + </div> +</body> +</html> |