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diff --git a/doc/dms.1 b/doc/dms.1 new file mode 100644 index 0000000..1ead9f2 --- /dev/null +++ b/doc/dms.1 @@ -0,0 +1,121 @@ +.\" 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\. |