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.TH "DMS" "1" "September 2017" "www.complex-networks.net" "www.complex-networks.net"
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.SH "NAME"
\fBdms\fR \- Grow a scale\-free random graph with tunable exponent
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.SH "SYNOPSIS"
\fBdms\fR \fIN\fR \fIm\fR \fIn0\fR \fIa\fR
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.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\.
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.SH "PARAMETERS"
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.TP
\fIN\fR
Number of nodes of the final graph\.
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.TP
\fIm\fR
Number of edges created by each new node\.
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.TP
\fIn0\fR
Number of nodes in the initial (seed) graph\.
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.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\.
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.SH "OUTPUT"
\fBdms\fR prints on STDOUT the edge list of the final graph\.
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.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
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.IP "" 4
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.nf

    gamma = 2\.5
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.fi
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.IP "" 0
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.P
Since \fBdms\fR produces graphs with scale\-free degree sequences with an exponent \fBgamma = 3\.0 + a/m\fR, the command:
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.IP "" 4
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.nf

    $ dms 10000 4 4 \-2\.0 > dms_10000_4_4_\-2\.0\.txt
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.fi
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.IP "" 0
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.P
will produce the desired network\. In fact, the average degree of the graph will be:
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.IP "" 4
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.nf

    <k> = 2m = 8
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.fi
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.IP "" 0
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.P
and the exponent of the power\-law degree distribution will be:
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.IP "" 4
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.nf

    gamma = 3\.0 + a/m = 3\.0 \-0\.5 = 2\.5
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.fi
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.IP "" 0
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.P
The following command:
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.IP "" 4
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.nf

    $ dms 10000 3 5 0 > dms_10000_3_5_0\.txt
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.fi
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.IP "" 0
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.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)\.
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.SH "SEE ALSO"
ba(1), bb_fitness(1)
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.SH "REFERENCES"
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.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\.
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.IP "\(bu" 4
V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 6, Cambridge University Press (2017)
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.IP "\(bu" 4
V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 13, Cambridge University Press (2017)
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.IP "" 0
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.SH "AUTHORS"
(c) Vincenzo \'KatolaZ\' Nicosia 2009\-2017 \fB<v\.nicosia@qmul\.ac\.uk>\fR\.