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
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
|
<!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>components(1) - Find the connected components 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'>components(1)</li>
<li class='tc'>www.complex-networks.net</li>
<li class='tr'>components(1)</li>
</ol>
<h2 id="NAME">NAME</h2>
<p class="man-name">
<code>components</code> - <span class="man-whatis">Find the connected components of a graph</span>
</p>
<h2 id="SYNOPSIS">SYNOPSIS</h2>
<p><code>components</code> <var>graph_in</var> [SHOW]</p>
<h2 id="DESCRIPTION">DESCRIPTION</h2>
<p><code>components</code> finds the connected components of the undirected graph
given as input using the Depth-First Search algorithm, and prints the
size of each of them. If the optional second parameter <code>SHOW</code> is
provided, the program dumps on output also the list of nodes belonging
to each component.</p>
<h2 id="PARAMETERS">PARAMETERS</h2>
<dl>
<dt><var>graph_in</var></dt><dd><p> input graph (edge list) if equal to <code>-</code> (dash), read the edge list
from STDIN.</p></dd>
<dt class="flush">SHOW</dt><dd><p> If the (optional) second parameter is equal to <code>SHOW</code>, the program
will dump on output the list of all the nodes belonging to each
connected component.</p></dd>
</dl>
<h2 id="OUTPUT">OUTPUT</h2>
<p><code>components</code> prints on the standard output the size of all the
connected components of the undirected graph given as input, one per
line:</p>
<pre><code>size_1
size_2
size_3
.....
</code></pre>
<p>where <code>size_1</code> is the size of the first component, <code>size_2</code> is the
size of the second component, and so on. Notice that the sizes are not
sorted. If <code>SHOW</code> is given, the program shows the list of nodes
belonging to each component, in the format:</p>
<pre><code>size_1: node_1 node_2 node_3 ...
size_2: node_1 node_2 node_3 ...
</code></pre>
<h2 id="EXAMPLES">EXAMPLES</h2>
<p>The following command:</p>
<pre><code> $ components er_1000_5000.txt
1000
$
</code></pre>
<p>shows on output the size of the only connected component of the graph
<code>er_1000_5000.txt</code>. In this case the graph has only one connected
component (it is a super-critical Erdos-Renyi random graph with 1000
nodes and 5000 edges). A more interesting example can be obtained
using the graph <code>er_1000_2000.txt</code>:</p>
<pre><code> $ components er_1000_2000.txt
985
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
$
</code></pre>
<p>In this case, the graph has 16 connected components: one of those
components contains 985 nodes, while the other 15 components consist
of isolated nodes. If we want to know who are the nodes belonging to
each connected component, we run:</p>
<pre><code> $ components er_1000_2000.txt SHOW
985: 0 1 2 3 4 5 6 7 8 9 10 11 12.....
...
1: 63
1: 75
1: 218
1: 222
1: 368
1: 398
1: 441
1: 566
1: 572
1: 663
1: 715
1: 756
1: 863
1: 883
1: 917
$
</code></pre>
<p>If we run:</p>
<pre><code> $ components er_1000_2000.txt SHOW > er_1000_2000.txt_components
</code></pre>
<p>the result of <code>components</code> will be saved in the file
<code>er_1000_2000.txt_components</code>.</p>
<h2 id="SEE-ALSO">SEE ALSO</h2>
<p><a class="man-ref" href="strong_conn.1.html">strong_conn<span class="s">(1)</span></a>, <a class="man-ref" href="node_components.1.html">node_components<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>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
Methods and Applications", Chapter 3, Cambridge University Press
(2017)</p></li>
<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
Methods and Applications", Appendix 8, 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'>components(1)</li>
</ol>
</div>
</body>
</html>
|
