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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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<ol class='man-decor man-head man head'>
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<li class='tl'>betweenness(1)</li>
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<li class='tc'>www.complex-networks.net</li>
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<li class='tr'>betweenness(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>betweenness</code> - <span class="man-whatis">Compute the betweenness centrality of nodes and edges</span>
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</p>
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<h2 id="SYNOPSIS">SYNOPSIS</h2>
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<p><code>betweenness</code> <var>graph_in</var> [ SEQ <var>node_start</var> [<var>node_end</var>]]</p>
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<p><code>betweenness</code> <var>graph_in</var> [ RND <var>num</var>]</p>
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<h2 id="DESCRIPTION">DESCRIPTION</h2>
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<p><code>betweenness</code> computes the betweenness centrality of all the nodes and
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edges of an undirected graph provided as input. The program implements
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the algorithm by U. Brandes, and computes the betweenness using all
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the shortest paths originating from a subset of the nodes of the
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graph, either in a sequence (if <em>SEQ</em> is the second parameter) or
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sampled unirofmly at random (if <em>RND</em> is the second parameter). If
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<var>graph_in</var> is the only parameter, <code>betweenness</code> takes into account all
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the shortest paths.</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><p> input graph (edge list) if equal to <code>-</code> (dash), read the edge list
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from STDIN.</p></dd>
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<dt><var>node_start</var></dt><dd><p> The label of the first node in a sequence of nodes (when <em>SEQ</em> is
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the second parameter).</p></dd>
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<dt><var>node_end</var></dt><dd><p> The label of the last node in a sequence of nodes (when <em>SEQ</em> is
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the second parameter).</p></dd>
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<dt class="flush"><var>num</var></dt><dd><p> The number of nodes to be considered (when <em>RND</em> is the second
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parameter)</p></dd>
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</dl>
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<h2 id="OUTPUT">OUTPUT</h2>
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<p><code>betweenness</code> prints on the standard output (STDOUT) the betweenness
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centrality of all the nodes, starting from the node with label 0, and
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on the standard error (STDERR) the betweenness centrality of all the
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edges, one edge per line, in the format:</p>
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<pre><code>node1 node2 bet_score
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</code></pre>
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<h2 id="EXAMPLES">EXAMPLES</h2>
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<p>The following command:</p>
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<pre><code> $ betweenness er_1000_5000.txt >node_bet 2>edge_bet
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</code></pre>
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<p>computes the node and edge betweenness centrality of the graph
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<code>er_1000_5000.txt</code>, using all the shortest paths. Since we used the
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redirections <code>>node_bet</code> and <code>2>edge_bet</code>, the values of node and edge
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betweenness will be saved in the files <code>node_bet</code> and <code>edge_bet</code>,
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respectively.</p>
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<p>The command:</p>
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<pre><code> $ betweenness er_1000_5000.txt SEQ 100 200 2>edge_bet_100_200
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</code></pre>
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<p>will compute the betweenness of nodes and edges in the graph
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<code>er_1000_5000.txt</code>, based only on the shortest paths originating from
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the nodes whose labels are in the range [100,200]. The node
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betweenness will be printed on STDOUT, while the edge betweenness will
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be saved in the file <code>edge_bet_100_200</code>.</p>
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<p>Finally, the command:</p>
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<pre><code> $ betweenness er_1000_5000.txt RND 250 >node_bet_RND
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</code></pre>
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<p>will compute the betweenness centrality based on the shortest paths
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originating from 250 nodes in the graph, sampled uniformly at
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random. The node betweenness is saved in the file <code>node_bet_RND</code>,
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while the values of edge betweenness are printed on STDOUT.</p>
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<h2 id="SEE-ALSO">SEE ALSO</h2>
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<p><span class="man-ref">bet_dependency<span class="s">(1)</span></span>, <span class="man-ref">shortest<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>U. Brandes. "A Faster Algorithm for Betweenness Centrality".
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J. Math. Sociol. 25 (2001), 163-177.</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 6, 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", Appendix 7, 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'>betweenness(1)</li>
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</ol>
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