extended_barabasi_albert_graph#

extended_barabasi_albert_graph(n, m, p, q, seed=None, *, create_using=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.

create_usingGraph constructor, optional (default=nx.Graph)

Graph type to create. If graph instance, then cleared before populated. Multigraph and directed types are not supported and raise a NetworkXError.

Returns:

GGraph

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.