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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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+ <title>conf_model_deg(1) - Sample a simple graph from the configuration model</title>
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+<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'>conf_model_deg(1)</li>
+ <li class='tc'>www.complex-networks.net</li>
+ <li class='tr'>conf_model_deg(1)</li>
+ </ol>
+
+ <h2 id="NAME">NAME</h2>
+<p class="man-name">
+ <code>conf_model_deg</code> - <span class="man-whatis">Sample a simple graph from the configuration model</span>
+</p>
+
+<h2 id="SYNOPSIS">SYNOPSIS</h2>
+
+<p><code>conf_model_deg</code> <var>degs</var> [<var>threshold</var>]</p>
+
+<h2 id="DESCRIPTION">DESCRIPTION</h2>
+
+<p><code>conf_model_deg</code> samples a simple random undirected graph (i.e., a
+graph without self-loops and multiple edges) from the configuration
+model associated to the degree sequence provided in the input file
+<var>degs</var>.</p>
+
+<h2 id="PARAMETERS">PARAMETERS</h2>
+
+<dl>
+<dt class="flush"><var>degs</var></dt><dd><p> The name of the file containing the degree sequence. If <var>degs</var> is
+ equal to '-' (dash) the degree sequence is read from STDIN
+ (standard input).</p></dd>
+<dt><var>threshold</var>:</dt><dd><p></p>
+
+<p> Optional number of edge stubs that are allowed to remain
+ unmatched. This is useful to create graphs from too-constrained
+ degree sequences (see <a href="#EXAMPLES" title="EXAMPLES" data-bare-link="true">EXAMPLES</a> below).</p></dd>
+</dl>
+
+
+<h2 id="OUTPUT">OUTPUT</h2>
+
+<p><code>conf_model_deg</code> prints on output the edge list of the sampled graph,
+and reports on STDERR whether it has been able to find a graph.</p>
+
+<h2 id="EXAMPLES">EXAMPLES</h2>
+
+<p>Let us assume that the file <code>pl_-3.0_3_500_10000</code> contains a power-law
+degree sequence ('gamma=-3.0', 'k_min=3', 'k_max=500', 'N=10000'), for
+instance created using <a href="power_law.1.html">power_law(1)</a>. We can sample a
+simple configuration model graph having that degree sequence using:</p>
+
+<pre><code> $ conf_model_deg pl_-3.0_3_500_10000 &gt; conf_model_-3.0_3_500_10000.net
+</code></pre>
+
+<p>where we have redirected the output (the resulting edge list) to the
+file <code>conf_model_-3.0_3_500_10000.net</code>. In this case it is not
+necessary to specify a threshold, since the maximum degree in the
+sequence is 126, which is smaller than the structural cut-off.</p>
+
+<p>Let us assume now that the file <code>AS-20010316.net_degs</code> contains the
+degree sequence of the data set <code>AS-20010316.net</code> (the graph of the
+Internet at AS level in March 2001). In this case, the degree sequence
+is too constrained, since the maximum degree (2277) is much larger
+than the structural cut-off (see <a href="#REFERENCES" title="REFERENCES" data-bare-link="true">REFERENCES</a> below). So if we don't
+specify a threshold, we get:</p>
+
+<pre><code> $ conf_model_deg AS-20010316.net_degs &gt; AS_20010316_rand.net
+ Graph not found (unmatched stubs: 986 &gt; threshold: 0)
+ Graph not found (unmatched stubs: 888 &gt; threshold: 0)
+ Graph not found (unmatched stubs: 974 &gt; threshold: 0)
+ .....
+</code></pre>
+
+<p>and so on, since <code>conf_model_deg</code> is trying to match all the edge
+stubs, without success. From the messages printed by <code>conf_model_deg</code>
+on STDERR we notice that the number of unmatched stubs is 986 in the
+first attempt, 888 in the second one, and so on, while the acceptable
+threshold is set to 0. If we instead specify a reasonable threshold
+(in this example set to 950):</p>
+
+<pre><code> $ conf_model_deg AS-20010316.net_degs 950 &gt; AS_20010316_rand.net
+ Graph not found (unmatched stubs: 978 &gt; threshold: 950)
+ Found a graph (unmatched stubs: 876 &lt;= threshold: 950)
+ $
+</code></pre>
+
+<p><code>conf_model_deg</code> is able to create a graph after a few
+attempts. Notice that in the resulting graph 876 of the original edge
+stubs will remain unmatched, meaning that the resulting graph has
+876/2=438 edges less than those contained in the original graph.</p>
+
+<h2 id="SEE-ALSO">SEE ALSO</h2>
+
+<p><a class="man-ref" href="deg_seq.1.html">deg_seq<span class="s">(1)</span></a>, <a class="man-ref" href="conf_model_deg_nocheck.1.html">conf_model_deg_nocheck<span class="s">(1)</span></a>, <a class="man-ref" href="power_law.1.html">power_law<span class="s">(1)</span></a>, <a class="man-ref" href="hv_net.1.html">hv_net<span class="s">(1)</span></a></p>
+
+<h2 id="REFERENCES">REFERENCES</h2>
+
+<ul>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Chapter 5, Cambridge University Press
+(2017)</p></li>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Appendix 12, Cambridge University Press
+(2017)</p></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'>conf_model_deg(1)</li>
+ </ol>
+
+ </div>
+</body>
+</html>