fast_gnp_random_graph

fast_gnp_random_graph(n, p, seed=None, directed=False)

Returns a \(G_{n,p}\) random graph, also known as an Erdős-Rényi graph or a binomial graph.

Parameters:

nint

The number of nodes.

pfloat

Probability for edge creation.

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

directedbool, optional (default=False)

If True, this function returns a directed graph.

See also

gnp_random_graph

Notes

The \(G_{n,p}\) graph algorithm chooses each of the \([n (n - 1)] / 2\) (undirected) or \(n (n - 1)\) (directed) possible edges with probability \(p\).

This algorithm [1] runs in \(O(n + m)\) time, where m is the expected number of edges, which equals \(p n (n - 1) / 2\). This should be faster than gnp_random_graph() when \(p\) is small and the expected number of edges is small (that is, the graph is sparse).

References

[1]

Vladimir Batagelj and Ulrik Brandes, “Efficient generation of large random networks”, Phys. Rev. E, 71, 036113, 2005.