1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
|
<!DOCTYPE html>
<html>
<head>
<meta http-equiv='content-type' value='text/html;charset=utf8'>
<meta name='generator' value='Ronn/v0.7.3 (http://github.com/rtomayko/ronn/tree/0.7.3)'>
<title>kruskal(1) - Find the minimum/maximum spanning tree of a graph</title>
<style type='text/css' media='all'>
/* style: man */
body#manpage {margin:0}
.mp {max-width:100ex;padding:0 9ex 1ex 4ex}
.mp p,.mp pre,.mp ul,.mp ol,.mp dl {margin:0 0 20px 0}
.mp h2 {margin:10px 0 0 0}
.mp > p,.mp > pre,.mp > ul,.mp > ol,.mp > dl {margin-left:8ex}
.mp h3 {margin:0 0 0 4ex}
.mp dt {margin:0;clear:left}
.mp dt.flush {float:left;width:8ex}
.mp dd {margin:0 0 0 9ex}
.mp h1,.mp h2,.mp h3,.mp h4 {clear:left}
.mp pre {margin-bottom:20px}
.mp pre+h2,.mp pre+h3 {margin-top:22px}
.mp h2+pre,.mp h3+pre {margin-top:5px}
.mp img {display:block;margin:auto}
.mp h1.man-title {display:none}
.mp,.mp code,.mp pre,.mp tt,.mp kbd,.mp samp,.mp h3,.mp h4 {font-family:monospace;font-size:14px;line-height:1.42857142857143}
.mp h2 {font-size:16px;line-height:1.25}
.mp h1 {font-size:20px;line-height:2}
.mp {text-align:justify;background:#fff}
.mp,.mp code,.mp pre,.mp pre code,.mp tt,.mp kbd,.mp samp {color:#131211}
.mp h1,.mp h2,.mp h3,.mp h4 {color:#030201}
.mp u {text-decoration:underline}
.mp code,.mp strong,.mp b {font-weight:bold;color:#131211}
.mp em,.mp var {font-style:italic;color:#232221;text-decoration:none}
.mp a,.mp a:link,.mp a:hover,.mp a code,.mp a pre,.mp a tt,.mp a kbd,.mp a samp {color:#0000ff}
.mp b.man-ref {font-weight:normal;color:#434241}
.mp pre {padding:0 4ex}
.mp pre code {font-weight:normal;color:#434241}
.mp h2+pre,h3+pre {padding-left:0}
ol.man-decor,ol.man-decor li {margin:3px 0 10px 0;padding:0;float:left;width:33%;list-style-type:none;text-transform:uppercase;color:#999;letter-spacing:1px}
ol.man-decor {width:100%}
ol.man-decor li.tl {text-align:left}
ol.man-decor li.tc {text-align:center;letter-spacing:4px}
ol.man-decor li.tr {text-align:right;float:right}
</style>
<style type='text/css' media='all'>
/* style: toc */
.man-navigation {display:block !important;position:fixed;top:0;left:113ex;height:100%;width:100%;padding:48px 0 0 0;border-left:1px solid #dbdbdb;background:#eee}
.man-navigation a,.man-navigation a:hover,.man-navigation a:link,.man-navigation a:visited {display:block;margin:0;padding:5px 2px 5px 30px;color:#999;text-decoration:none}
.man-navigation a:hover {color:#111;text-decoration:underline}
</style>
</head>
<!--
The following styles are deprecated and will be removed at some point:
div#man, div#man ol.man, div#man ol.head, div#man ol.man.
The .man-page, .man-decor, .man-head, .man-foot, .man-title, and
.man-navigation should be used instead.
-->
<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'>kruskal(1)</li>
<li class='tc'>www.complex-networks.net</li>
<li class='tr'>kruskal(1)</li>
</ol>
<h2 id="NAME">NAME</h2>
<p class="man-name">
<code>kruskal</code> - <span class="man-whatis">Find the minimum/maximum spanning tree of a graph</span>
</p>
<h2 id="SYNOPSIS">SYNOPSIS</h2>
<p><code>kruskal</code> <var>graph_in</var> [MAX]</p>
<h2 id="DESCRIPTION">DESCRIPTION</h2>
<p><code>kruskal</code> computes the minimum (or maximum) spanning tree of
<var>graph_in</var>, using the Kruskal's algorithm. 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><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>
<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>
|
