fast_gnp_random_graph#

fast_gnp_random_graph(n, p, seed=None, directed=False)[source]#

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.