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If <var>grahp_in</var> is +unweighted, <code>kruskal</code> computes one of the spanning trees of the +graph. The program prints on output the (weighted) edge list of the +spanning tree.</p> + +<h2 id="PARAMETERS">PARAMETERS</h2> + +<dl> +<dt><var>graph_in</var></dt><dd><p> undirected input graph (edge list). It must be an existing file.</p></dd> +<dt class="flush"><code>MAX</code></dt><dd><p> If the second (optional) parameter is equal to <code>MAX</code>, compute the + maximum spanning tree. Otherwise, compute the minimum spanning tree.</p></dd> +</dl> + + +<h2 id="OUTPUT">OUTPUT</h2> + +<p>The program prints on STDOUT the edge list of the minimum (maximum) +spannig tree of <var>graph_in</var>, in the format:</p> + +<pre><code> i_1 j_1 w_ij_1 + i_2 j_2 w_ij_2 + .... +</code></pre> + +<h2 id="EXAMPLES">EXAMPLES</h2> + +<p>To find the minimum spanning tree of the graph <code>stocks_62_weight.net</code> +(the network of stocks in the New York Exchange market) we use the +command:</p> + +<pre><code> $ kruskal stocks_62_weight.net + 52 53 0.72577357 + 43 53 0.72838212 + 2 53 0.72907212 + ... + 36 53 0.7973488 + 53 58 0.79931683 + 26 27 0.8029602 + $ +</code></pre> + +<p>which prints on output the edge list of the minimum spanning tree. +However, since the weight of each edge in that graph indicates the +similarity in the behaviour of two stocks, the maximum spanning tree +contains information about the backbone of similarities among +stocks. To obtain the maximum spannin tree, we just specify <code>MAX</code> as +second parameter:</p> + +<pre><code> $ kruskal stocks_62_weight.net MAX + 56 58 1.523483 + 2 52 1.3826744 + 32 51 1.3812241 + ... + 33 55 0.86880272 + 7 28 0.8631584 + 1 53 0.81876166 + $ +</code></pre> + +<h2 id="SEE-ALSO">SEE ALSO</h2> + +<p><a class="man-ref" href="clust_w.1.html">clust_w<span class="s">(1)</span></a>, <a class="man-ref" href="dijkstra.1.html">dijkstra<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>J. B. Kruskal. "On the shortest spanning subtree of a graph and the +traveling sales-man problem". P. Am. Math. Soc. 7 (1956), +48-48.</p></li> +<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, +Methods and Applications", Appendix 20, Cambridge University Press +(2017)</p></li> +<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, +Methods and Applications", Chapter 10, Cambridge University Press +(2017)</p></li> +</ul> + + +<h2 id="AUTHORS">AUTHORS</h2> + +<p>(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <code><v.nicosia@qmul.ac.uk></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'>kruskal(1)</li> + </ol> + + </div> +</body> +</html> |