1. dms(1)
  2. www.complex-networks.net
  3. dms(1)

NAME

dms - Grow a scale-free random graph with tunable exponent

SYNOPSIS

dms N m n0 a

DESCRIPTION

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.

PARAMETERS

N

Number of nodes of the final graph.

m

Number of edges created by each new node.

n0

Number of nodes in the initial (seed) graph.

a

This parameter sets the exponent of the degree distribution (gamma = 3.0 + a/m). a must be larger than -m.

OUTPUT

dms prints on STDOUT the edge list of the final graph.

EXAMPLES

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 >).

SEE ALSO

ba(1), bb_fitness(1)

REFERENCES

AUTHORS

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.

  1. www.complex-networks.net
  2. September 2017
  3. dms(1)