# extended_barabasi_albert_graph#

extended_barabasi_albert_graph(n, m, p, q, seed=None)[source]#

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 model.

Parameters:
nint

Number of nodes

mint

Number of edges with which a new node attaches to existing nodes

pfloat

Probability value for adding an edge between existing nodes. p + q < 1

qfloat

Probability value of rewiring of existing edges. p + q < 1

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

Returns:
GGraph
Raises:
NetworkXError

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

References



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