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.
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 >
).
ba(1), bb_fitness(1)
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>
.