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authorKatolaZ <katolaz@freaknet.org>2017-09-27 15:06:31 +0100
committerKatolaZ <katolaz@freaknet.org>2017-09-27 15:06:31 +0100
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+.\" generated with Ronn/v0.7.3
+.\" http://github.com/rtomayko/ronn/tree/0.7.3
+.
+.TH "DMS" "1" "September 2017" "www.complex-networks.net" "www.complex-networks.net"
+.
+.SH "NAME"
+\fBdms\fR \- Grow a scale\-free random graph with tunable exponent
+.
+.SH "SYNOPSIS"
+\fBdms\fR \fIN\fR \fIm\fR \fIn0\fR \fIa\fR
+.
+.SH "DESCRIPTION"
+\fBdms\fR grows an undirected random scale\-free graph with \fIN\fR nodes using the modified linear preferential attachment model proposed by Dorogovtsev, Mendes and Samukhin\. The initial network is a clique of \fIn0\fR nodes, and each new node creates \fIm\fR new edges\. The resulting graph will have a scale\-free degree distribution, whose exponent converges to \fBgamma=3\.0 + a/m\fR for large \fIN\fR\.
+.
+.SH "PARAMETERS"
+.
+.TP
+\fIN\fR
+Number of nodes of the final graph\.
+.
+.TP
+\fIm\fR
+Number of edges created by each new node\.
+.
+.TP
+\fIn0\fR
+Number of nodes in the initial (seed) graph\.
+.
+.TP
+\fIa\fR
+This parameter sets the exponent of the degree distribution (\fBgamma = 3\.0 + a/m\fR)\. \fIa\fR must be larger than \fI\-m\fR\.
+.
+.SH "OUTPUT"
+\fBdms\fR prints on STDOUT the edge list of the final graph\.
+.
+.SH "EXAMPLES"
+Let us assume that we want to create a scale\-free network with \fIN=10000\fR nodes, with average degree equal to 8, whose degree distribution has exponent
+.
+.IP "" 4
+.
+.nf
+
+ gamma = 2\.5
+.
+.fi
+.
+.IP "" 0
+.
+.P
+Since \fBdms\fR produces graphs with scale\-free degree sequences with an exponent \fBgamma = 3\.0 + a/m\fR, the command:
+.
+.IP "" 4
+.
+.nf
+
+ $ dms 10000 4 4 \-2\.0 > dms_10000_4_4_\-2\.0\.txt
+.
+.fi
+.
+.IP "" 0
+.
+.P
+will produce the desired network\. In fact, the average degree of the graph will be:
+.
+.IP "" 4
+.
+.nf
+
+ <k> = 2m = 8
+.
+.fi
+.
+.IP "" 0
+.
+.P
+and the exponent of the power\-law degree distribution will be:
+.
+.IP "" 4
+.
+.nf
+
+ gamma = 3\.0 + a/m = 3\.0 \-0\.5 = 2\.5
+.
+.fi
+.
+.IP "" 0
+.
+.P
+The following command:
+.
+.IP "" 4
+.
+.nf
+
+ $ dms 10000 3 5 0 > dms_10000_3_5_0\.txt
+.
+.fi
+.
+.IP "" 0
+.
+.P
+creates a scale\-free graph with \fIN=10000\fR nodes, where each new node creates \fIm=3\fR new edges and the initial seed network is a ring of \fIn0=5\fR nodes\. The degree distribution of the final graph will have exponent equal to \fBgamma = 3\.0 + a/m = 3\.0\fR\. In this case, \fBdms\fR produces a Barabasi\-Albert graph (see ba(1) for details)\. The edge list of the graph is saved in the file \fBdms_10000_3_5_0\.txt\fR (thanks to the redirection operator \fB>\fR)\.
+.
+.SH "SEE ALSO"
+ba(1), bb_fitness(1)
+.
+.SH "REFERENCES"
+.
+.IP "\(bu" 4
+S\. N\. Dorogovtsev, J\. F\. F\. Mendes, A\. N\. Samukhin\. "Structure of Growing Networks with Preferential Linking"\. Phys\. Rev\. Lett\. 85 (2000), 4633\-4636\.
+.
+.IP "\(bu" 4
+V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 6, Cambridge University Press (2017)
+.
+.IP "\(bu" 4
+V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 13, Cambridge University Press (2017)
+.
+.IP "" 0
+.
+.SH "AUTHORS"
+(c) Vincenzo \'KatolaZ\' Nicosia 2009\-2017 \fB<v\.nicosia@qmul\.ac\.uk>\fR\.