# networkx.generators.random_graphs.erdos_renyi_graph¶

erdos_renyi_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.

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

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.

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.

>>> nx.binomial_graph is nx.gnp_random_graph
True
>>> nx.erdos_renyi_graph is nx.gnp_random_graph
True


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).