glp_topology(n, m, m0, p, beta, seed=None)[source]

Return a random topology using the Generalized Linear Preference (GLP) preferential attachment model.

It differs from the extended Barabasi-Albert model in that there is link rewiring and a beta parameter is introduced to fine-tune preferential attachment.

More precisely, the GLP topology is built as follows. First, a line topology with m0 nodes is created. Then, at each step: with probability p, add m new links between existing nodes, selected with probability:

\Pi(i) = \frac{deg(i) - \beta 1}{\sum_{v \in V} (deg(v) - \beta)}

with probability 1-p, add a new node and attach it to m nodes of the existing topology selected with probability \Pi(i)

Repeat the previous step until the topology comprises n nodes in total.

n : int

Number of nodes

m : int

Number of edges to attach from a new node to existing nodes

m0 : int

Number of edges initially attached to the network

p : float

The probability that new links are added

beta : float

Parameter to fine-tune preferntial attachment: beta < 1

seed : int, optional

Seed for random number generator (default=None).

G : Topology


[1]T. Bu and D. Towsey “On distinguishing between Internet power law topology generators”, Proceeding od the 21st IEEE INFOCOM conference. IEEE, volume 2, pages 638-647, 2002.