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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>components(1) - Find the connected components of a graph</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'>components(1)</li>
+ <li class='tc'>www.complex-networks.net</li>
+ <li class='tr'>components(1)</li>
+ </ol>
+
+ <h2 id="NAME">NAME</h2>
+<p class="man-name">
+ <code>components</code> - <span class="man-whatis">Find the connected components of a graph</span>
+</p>
+
+<h2 id="SYNOPSIS">SYNOPSIS</h2>
+
+<p><code>components</code> <var>graph_in</var> [SHOW]</p>
+
+<h2 id="DESCRIPTION">DESCRIPTION</h2>
+
+<p><code>components</code> finds the connected components of the undirected graph
+given as input using the Depth-First Search algorithm, and prints the
+size of each of them. If the optional second parameter <code>SHOW</code> is
+provided, the program dumps on output also the list of nodes belonging
+to each component.</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.</p></dd>
+<dt class="flush">SHOW</dt><dd><p> If the (optional) second parameter is equal to <code>SHOW</code>, the program
+ will dump on output the list of all the nodes belonging to each
+ connected component.</p></dd>
+</dl>
+
+
+<h2 id="OUTPUT">OUTPUT</h2>
+
+<p><code>components</code> prints on the standard output the size of all the
+connected components of the undirected graph given as input, one per
+line:</p>
+
+<pre><code>size_1
+size_2
+size_3
+.....
+</code></pre>
+
+<p>where <code>size_1</code> is the size of the first component, <code>size_2</code> is the
+size of the second component, and so on. Notice that the sizes are not
+sorted. If <code>SHOW</code> is given, the program shows the list of nodes
+belonging to each component, in the format:</p>
+
+<pre><code>size_1: node_1 node_2 node_3 ...
+size_2: node_1 node_2 node_3 ...
+</code></pre>
+
+<h2 id="EXAMPLES">EXAMPLES</h2>
+
+<p>The following command:</p>
+
+<pre><code> $ components er_1000_5000.txt
+ 1000
+ $
+</code></pre>
+
+<p>shows on output the size of the only connected component of the graph
+<code>er_1000_5000.txt</code>. In this case the graph has only one connected
+component (it is a super-critical Erdos-Renyi random graph with 1000
+nodes and 5000 edges). A more interesting example can be obtained
+using the graph <code>er_1000_2000.txt</code>:</p>
+
+<pre><code> $ components er_1000_2000.txt
+ 985
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
+ $
+</code></pre>
+
+<p>In this case, the graph has 16 connected components: one of those
+components contains 985 nodes, while the other 15 components consist
+of isolated nodes. If we want to know who are the nodes belonging to
+each connected component, we run:</p>
+
+<pre><code> $ components er_1000_2000.txt SHOW
+ 985: 0 1 2 3 4 5 6 7 8 9 10 11 12.....
+ ...
+ 1: 63
+ 1: 75
+ 1: 218
+ 1: 222
+ 1: 368
+ 1: 398
+ 1: 441
+ 1: 566
+ 1: 572
+ 1: 663
+ 1: 715
+ 1: 756
+ 1: 863
+ 1: 883
+ 1: 917
+ $
+</code></pre>
+
+<p>If we run:</p>
+
+<pre><code> $ components er_1000_2000.txt SHOW &gt; er_1000_2000.txt_components
+</code></pre>
+
+<p>the result of <code>components</code> will be saved in the file
+<code>er_1000_2000.txt_components</code>.</p>
+
+<h2 id="SEE-ALSO">SEE ALSO</h2>
+
+<p><a class="man-ref" href="strong_conn.1.html">strong_conn<span class="s">(1)</span></a>, <a class="man-ref" href="node_components.1.html">node_components<span class="s">(1)</span></a>, <a class="man-ref" href="largest_component.1.html">largest_component<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 3, Cambridge University Press
+(2017)</p></li>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Appendix 8, 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'>components(1)</li>
+ </ol>
+
+ </div>
+</body>
+</html>