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binomial_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.

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

  • n (int) – The number of nodes.
  • p (float) – Probability for edge creation.
  • seed (int, optional) – Seed for random number generator (default=None).
  • directed (bool, optional (default=False)) – If True, this function returns a directed graph.


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


  1. Erdős and A. Rényi, On Random Graphs, Publ. Math. 6, 290 (1959).
    1. Gilbert, Random Graphs, Ann. Math. Stat., 30, 1141 (1959).