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<title>kruskal(1) - Find the minimum/maximum spanning tree of a graph</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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<ol class='man-decor man-head man head'>
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<li class='tl'>kruskal(1)</li>
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<li class='tc'>www.complex-networks.net</li>
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<li class='tr'>kruskal(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>kruskal</code> - <span class="man-whatis">Find the minimum/maximum spanning tree of a graph</span>
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</p>
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<h2 id="SYNOPSIS">SYNOPSIS</h2>
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<p><code>kruskal</code> <var>graph_in</var> [MAX]</p>
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<h2 id="DESCRIPTION">DESCRIPTION</h2>
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<p><code>kruskal</code> computes the minimum (or maximum) spanning tree of
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<var>graph_in</var>, using the Kruskal's algorithm. If <var>grahp_in</var> is
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unweighted, <code>kruskal</code> computes one of the spanning trees of the
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graph. The program prints on output the (weighted) edge list of the
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spanning tree.</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> undirected input graph (edge list). It must be an existing file.</p></dd>
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<dt class="flush"><code>MAX</code></dt><dd><p> If the second (optional) parameter is equal to <code>MAX</code>, compute the
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maximum spanning tree. Otherwise, compute the minimum spanning tree.</p></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 edge list of the minimum (maximum)
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spannig tree of <var>graph_in</var>, in the format:</p>
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<pre><code> i_1 j_1 w_ij_1
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i_2 j_2 w_ij_2
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....
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</code></pre>
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<h2 id="EXAMPLES">EXAMPLES</h2>
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<p>To find the minimum spanning tree of the graph <code>stocks_62_weight.net</code>
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(the network of stocks in the New York Exchange market) we use the
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command:</p>
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<pre><code> $ kruskal stocks_62_weight.net
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52 53 0.72577357
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43 53 0.72838212
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2 53 0.72907212
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...
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36 53 0.7973488
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53 58 0.79931683
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26 27 0.8029602
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$
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</code></pre>
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<p>which prints on output the edge list of the minimum spanning tree.
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However, since the weight of each edge in that graph indicates the
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similarity in the behaviour of two stocks, the maximum spanning tree
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contains information about the backbone of similarities among
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stocks. To obtain the maximum spannin tree, we just specify <code>MAX</code> as
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second parameter:</p>
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<pre><code> $ kruskal stocks_62_weight.net MAX
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56 58 1.523483
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2 52 1.3826744
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32 51 1.3812241
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...
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33 55 0.86880272
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7 28 0.8631584
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1 53 0.81876166
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$
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</code></pre>
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<h2 id="SEE-ALSO">SEE ALSO</h2>
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<p><span class="man-ref">clust_w<span class="s">(1)</span></span>, <span class="man-ref">dijkstra<span class="s">(1)</span></span>, <span class="man-ref">largest_component<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>J. B. Kruskal. "On the shortest spanning subtree of a graph and the
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traveling sales-man problem". P. Am. Math. Soc. 7 (1956),
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48-48.</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 20, 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 10, 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'>kruskal(1)</li>
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</ol>
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</body>
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