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<title>gn(1) - Find communities using the Girvan-Newman algorithm</title>
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<a href="#NAME">NAME</a>
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<a href="#SYNOPSIS">SYNOPSIS</a>
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<a href="#DESCRIPTION">DESCRIPTION</a>
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<a href="#PARAMETERS">PARAMETERS</a>
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<a href="#OUTPUT">OUTPUT</a>
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<a href="#EXAMPLES">EXAMPLES</a>
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<a href="#SEE-ALSO">SEE ALSO</a>
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<a href="#REFERENCES">REFERENCES</a>
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<a href="#AUTHORS">AUTHORS</a>
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<ol class='man-decor man-head man head'>
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<li class='tl'>gn(1)</li>
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<li class='tc'>www.complex-networks.net</li>
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<li class='tr'>gn(1)</li>
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</ol>
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<h2 id="NAME">NAME</h2>
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<p class="man-name">
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<code>gn</code> - <span class="man-whatis">Find communities using the Girvan-Newman algorithm</span>
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</p>
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<h2 id="SYNOPSIS">SYNOPSIS</h2>
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<p><code>gn</code> <var>graph_in</var></p>
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<h2 id="DESCRIPTION">DESCRIPTION</h2>
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<p><code>gn</code> finds the communities in <var>graph_in</var> using the Girvan-Newman
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algorithm, based on the successive removal of edges with high
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betweenness. The program prints on STDOUT the partition corresponding
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to the highest value of the modularity function, and reports on STDERR
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the number of communities after each edge removal and the
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corresponding value of modularity.</p>
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<p><code>N.B.</code>: the program recomputes the edge betweenness of the graph after
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the removal of each edge, so it is not feasible to use it on large
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graphs.</p>
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<h2 id="PARAMETERS">PARAMETERS</h2>
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<dl>
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<dt><var>graph_in</var></dt><dd> undirected input graph (edge list). If is equal to <code>-</code> (dash), read
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the edge list from STDIN.</dd>
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</dl>
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<h2 id="OUTPUT">OUTPUT</h2>
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<p>The program prints on STDOUT the partition corresponding to the
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highest value of modularity, in the format:</p>
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<pre><code> ## nc: NUM_COMM Q_max: Q_MAX
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node_1 comm_1
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node_2 comm_2
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node_3 comm_3
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...
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</code></pre>
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<p>where <code>comm_i</code> is the community to which <code>node_i</code> belongs. The first
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output line reports the number of communities <code>NUM_COMM</code> and the
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corresponding value of modularity <code>Q_MAX</code> of the partition.</p>
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<p>The program prints on STDERR the number of communities (connected
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components) after the removal of each edge, and the corresponding
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value of modularity, in the format:</p>
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<pre><code> nc_1 Q_1
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nc_2 Q_2
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nc_3 Q_3
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....
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</code></pre>
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<p>where <code>nc_i</code> is the number of communities after the i-th edge has been
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removed and <code>Q_i</code> is the corresponding value of modularity.</p>
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<h2 id="EXAMPLES">EXAMPLES</h2>
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<p>We can use <code>gn</code> to find communities in the graph <code>karate_club_unweighted.txt</code>
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(Zachary Karate Club network) with the command:</p>
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<pre><code> $ gn karate_club_unweighted.net 2> karate_gn_trace
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### nc: 4 Q_max: 0.365631
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0 1
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1 1
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2 2
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3 1
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4 3
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5 3
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6 3
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...
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30 2
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31 2
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32 2
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33 2
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$
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</code></pre>
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<p>In this run, the command has found a partition with 4 communities
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corrisponding to a modularity Q=0.365631. Notice that node 0, 1, 3,
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are in community 1, node 2 is in community 2, node 4,5,6, are in
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community 3 and so forth. In general, different runs will provide
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different partitions, since any tie in betweenness values is broke by
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choosing one of the edges with equal betweenness uniformly at
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random. In this example, we have chosen to save the information about
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number of communities and modularity after each edge removal in the
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file <code>karate_gn_trace</code>.</p>
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<h2 id="SEE-ALSO">SEE ALSO</h2>
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<p><span class="man-ref">modularity<span class="s">(1)</span></span>, <span class="man-ref">cnm<span class="s">(1)</span></span>, <span class="man-ref">label_prop<span class="s">(1)</span></span></p>
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<h2 id="REFERENCES">REFERENCES</h2>
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<ul>
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<li><p>M. Girvan and M. E. J. Newman. "Community structure in social and
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biological networks". P. Natl. Acad. Sci. USA 99 (2002), 7821--7826.</p></li>
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<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Appendix 17, Cambridge University Press
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(2017)</p></li>
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<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Chapter 9, Cambridge University Press
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(2017)</p></li>
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</ul>
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<h2 id="AUTHORS">AUTHORS</h2>
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<p>(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <code><v.nicosia@qmul.ac.uk></code>.</p>
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<ol class='man-decor man-foot man foot'>
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<li class='tl'>www.complex-networks.net</li>
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<li class='tc'>September 2017</li>
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<li class='tr'>gn(1)</li>
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</ol>
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