fast_gnp_random_graph#

fast_gnp_random_graph(n, p, seed=None, directed=False, *, create_using=None)[source]#

Returns a $G_{n,p}$ random graph, also known as an Erdős-Rényi graph or a binomial graph.

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.

create_usingGraph constructor, optional (default=nx.Graph or nx.DiGraph)

Graph type to create. If graph instance, then cleared before populated. Multigraph types are not supported and raise a NetworkXError. By default NetworkX Graph or DiGraph are used depending on directed.

See also

gnp_random_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 $pn(n-1)/2$. 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).

References

[1]

Vladimir Batagelj and Ulrik Brandes, “Efficient generation of large random networks”, Phys. Rev. E, 71, 036113, 2005.