dms - Grow a scale-free random graph with tunable exponent
dms N m n0 a
dms grows an undirected random scale-free graph with N nodes using
the modified linear preferential attachment model proposed by
Dorogovtsev, Mendes and Samukhin. The initial network is a clique of
n0 nodes, and each new node creates m new edges. The resulting
graph will have a scale-free degree distribution, whose exponent
converges to gamma=3.0 + a/m for large N.
Number of nodes of the final graph.
Number of edges created by each new node.
Number of nodes in the initial (seed) graph.
This parameter sets the exponent of the degree distribution
(gamma = 3.0 + a/m). a must be larger than -m.
dms prints on STDOUT the edge list of the final graph.
Let us assume that we want to create a scale-free network with N=10000 nodes, with average degree equal to 8, whose degree distribution has exponent
gamma = 2.5
Since dms produces graphs with scale-free degree sequences with an
exponent gamma = 3.0 + a/m, the command:
$ dms 10000 4 4 -2.0 > dms_10000_4_4_-2.0.txt
will produce the desired network. In fact, the average degree of the graph will be:
<k> = 2m = 8
and the exponent of the power-law degree distribution will be:
gamma = 3.0 + a/m = 3.0 -0.5 = 2.5
The following command:
$ dms 10000 3 5 0 > dms_10000_3_5_0.txt
creates a scale-free graph with N=10000 nodes, where each new node
creates m=3 new edges and the initial seed network is a ring of
n0=5 nodes. The degree distribution of the final graph will have
exponent equal to gamma = 3.0 + a/m = 3.0. In this case, dms
produces a Barabasi-Albert graph (see ba(1) for details). The edge
list of the graph is saved in the file dms_10000_3_5_0.txt (thanks
to the redirection operator >).
S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin. "Structure of Growing Networks with Preferential Linking". Phys. Rev. Lett. 85 (2000), 4633-4636.
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 6, Cambridge University Press (2017)
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 13, Cambridge University Press (2017)
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.