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networkx.generators.random_graphs.extended_barabasi_albert_graph

extended_barabasi_albert_graph(n, m, p, q, seed=None)

Returns an extended Barabási–Albert model graph.

An extended Barabási–Albert model graph is a random graph constructed using preferential attachment. The extended model allows new edges, rewired edges or new nodes. Based on the probabilities $p$ and $q$ with $p + q < 1$, the growing behavior of the graph is determined as:

1) With $p$ probability, $m$ new edges are added to the graph, starting from randomly chosen existing nodes and attached preferentially at the other end.

2) With $q$ probability, $m$ existing edges are rewired by randomly choosing an edge and rewiring one end to a preferentially chosen node.

3) With $(1 - p - q)$ probability, $m$ new nodes are added to the graph with edges attached preferentially.

When $p = q = 0$, the model behaves just like the Barabási–Alber mo

Parameters:

• n (int) – Number of nodes
• m (int) – Number of edges with which a new node attaches to existing nodes
• p (float) – Probability value for adding an edge between existing nodes. p + q < 1
• q (float) – Probability value of rewiring of existing edges. p + q < 1
• seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.

Returns:

G

Return type:

Graph

Raises:

NetworkXError – If m does not satisfy 1 <= m < n or 1 >= p + q

References

[1]	Albert, R., & Barabási, A. L. (2000) Topology of evolving networks: local events and universality Physical review letters, 85(24), 5234.