Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

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
  • 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.

binomial_graph() and erdos_renyi_graph() are aliases for gnp_random_graph().

>>> 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).