# networkx.generators.random_graphs.gnp_random_graph¶

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.

The $$G_{n,p}$$ model chooses each of the possible edges with probability $$p$$.

The functions binomial_graph() and erdos_renyi_graph() are aliases of this function.

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

This algorithm 2 runs in $$O(n^2)$$ time. For sparse graphs (that is, for small values of $$p$$), fast_gnp_random_graph() is a faster algorithm.

References

1
1. Erdős and A. Rényi, On Random Graphs, Publ. Math. 6, 290 (1959).

2
1. Gilbert, Random Graphs, Ann. Math. Stat., 30, 1141 (1959).