fnss.topologies.randmodels.extended_barabasi_albert_topology

extended_barabasi_albert_topology(n, m, m0, p, q, seed=None)[source]

Return a random topology using the extended Barabasi-Albert preferential attachment model.

Differently from the original Barabasi-Albert model, this model takes into account the presence of local events, such as the addition of new links or the rewiring of existing links.

More precisely, the Barabasi-Albert topology is built as follows. First, a topology with m0 isolated 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) + 1}{\sum_{v \in V} (deg(v) + 1)}

with probability q rewire m links. Each link to be rewired is selected as follows: a node i is randomly selected and a link is randomly removed from it. The node i is then connected to a new node randomly selected with probability \Pi(i), with probability 1-p-q 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.

Parameters:
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

q : float

The probability that existing links are rewired

seed : int, optional

Seed for random number generator (default=None).
Returns:
G : Topology

References

[1]A. L. Barabasi and R. Albert “Topology of evolving networks: local events and universality”, Physical Review Letters 85(24), 2000.