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# networkx.generators.random_graphs.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: n (int) – The number of nodes. p (float) – Probability for edge creation. seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness. directed (bool, optional (default=False)) – If True, this function returns a directed 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.