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


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 >).


ba(1), bb_fitness(1)



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

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