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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="#EXAMPLES">EXAMPLES</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'>pm(1)</li>
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<li class='tc'>www.complex-networks.net</li>
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<li class='tr'>pm(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>pm</code> - <span class="man-whatis">Compute the leading eigenvalue and eigenvector of a graph</span>
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</p>
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<h2 id="SYNOPSIS">SYNOPSIS</h2>
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<p><code>pm</code> <var>graph_in</var> <var>is_dir</var> <var>eps</var></p>
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<h2 id="DESCRIPTION">DESCRIPTION</h2>
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<p><code>pm</code> computes the leading eigenvalue and the corresponding eigenvector
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of the matrix given as input, using the Power Method. In particular,
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this implementation uses the Rayleigh iteration, which allows faster
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convergence on undirected 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><p> input graph (edge list) if equal to <code>-</code> (dash), read the edge list
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from STDIN (standard input).</p></dd>
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<dt class="flush"><var>is_dir</var></dt><dd><p> set either to <code>0</code> (zero) for undirected graphs, or to <code>1</code> (one)
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for directed graphs.</p></dd>
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<dt class="flush"><var>eps</var></dt><dd><p> Required relative error on the approximation of the leading
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eigenvalue. The program terminates when the relative change in the
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approximation of the eigenvalue is smaller than <code>eps</code></p></dd>
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</dl>
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<h2 id="EXAMPLES">EXAMPLES</h2>
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<p>The following command:</p>
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<pre><code> $ pm er_1000_5000.net 0 0.0000001
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</code></pre>
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<p>computes the leading eigenvalue and the corresponding eigenvector of
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the undirected graph stored in the file <code>er_1000_5000.txt</code>. We can
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store the leading eigenvector in a file, e.g. by using the command:</p>
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<pre><code> $ pm er_1000_5000.net 0 0.0000001 > er_1000_5000.net_eig
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11.0335794552533
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$
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</code></pre>
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<p>which will save the leading eigenvector in the file
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<code>er_1000_5000.net_eig</code>, one component for each row, and shown on
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output the leading eigenvalue of the graph.</p>
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<h2 id="REFERENCES">REFERENCES</h2>
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<ul>
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<li>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Appendix 5, Cambridge University Press
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(2017)</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'>pm(1)</li>
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</ol>
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