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<div class="section" id="eigenvalues">
<span id="advanced-eigenvalues"></span><h1>Eigenvalues<a class="headerlink" href="#eigenvalues" title="Permalink to this headline">ΒΆ</a></h1>
<p>[<a class="reference external" href="../../_static/examples/eigenvalues.py">source code</a>]</p>
<div class="highlight-python"><div class="highlight"><pre><span class="c">#!/usr/bin/env python</span>
<span class="sd">"""</span>
<span class="sd">Create an G{n,m} random graph and compute the eigenvalues.</span>
<span class="sd">Requires numpy or LinearAlgebra package from Numeric Python.</span>
<span class="sd">Uses optional pylab plotting to produce histogram of eigenvalues.</span>
<span class="sd">"""</span>
<span class="n">__author__</span> <span class="o">=</span> <span class="s">"""Aric Hagberg (hagberg@lanl.gov)"""</span>
<span class="n">__credits__</span> <span class="o">=</span> <span class="s">""""""</span>
<span class="c"># Copyright (C) 2004-2006 by</span>
<span class="c"># Aric Hagberg <hagberg@lanl.gov></span>
<span class="c"># Dan Schult <dschult@colgate.edu></span>
<span class="c"># Pieter Swart <swart@lanl.gov></span>
<span class="c"># All rights reserved.</span>
<span class="c"># BSD license.</span>
<span class="kn">from</span> <span class="nn">networkx</span> <span class="kn">import</span> <span class="o">*</span>
<span class="k">try</span><span class="p">:</span>
<span class="kn">import</span> <span class="nn">numpy.linalg</span>
<span class="n">eigenvalues</span><span class="o">=</span><span class="n">numpy</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eigvals</span>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ImportError</span><span class="p">(</span><span class="s">"numpy can not be imported."</span><span class="p">)</span>
<span class="k">try</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="o">*</span>
<span class="k">except</span><span class="p">:</span>
<span class="k">pass</span>
<span class="n">n</span><span class="o">=</span><span class="mi">1000</span> <span class="c"># 1000 nodes</span>
<span class="n">m</span><span class="o">=</span><span class="mi">5000</span> <span class="c"># 5000 edges</span>
<span class="n">G</span><span class="o">=</span><span class="n">gnm_random_graph</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">m</span><span class="p">)</span>
<span class="n">L</span><span class="o">=</span><span class="n">generalized_laplacian</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="n">e</span><span class="o">=</span><span class="n">eigenvalues</span><span class="p">(</span><span class="n">L</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Largest eigenvalue:"</span><span class="p">,</span> <span class="nb">max</span><span class="p">(</span><span class="n">e</span><span class="p">))</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Smallest eigenvalue:"</span><span class="p">,</span> <span class="nb">min</span><span class="p">(</span><span class="n">e</span><span class="p">))</span>
<span class="c"># plot with matplotlib if we have it</span>
<span class="c"># shows "semicircle" distribution of eigenvalues</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">hist</span><span class="p">(</span><span class="n">e</span><span class="p">,</span><span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span> <span class="c"># histogram with 100 bins</span>
<span class="n">xlim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="c"># eigenvalues between 0 and 2</span>
<span class="n">show</span><span class="p">()</span>
<span class="k">except</span><span class="p">:</span>
<span class="k">pass</span>
</pre></div>
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