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).