random_degree_sequence_graph#

random_degree_sequence_graph(sequence, seed=None, tries=10)[source]#

Returns a simple random graph with the given degree sequence.

If the maximum degree $$d_m$$ in the sequence is $$O(m^{1/4})$$ then the algorithm produces almost uniform random graphs in $$O(m d_m)$$ time where $$m$$ is the number of edges.

Parameters
sequencelist of integers

Sequence of degrees

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

triesint, optional

Maximum number of tries to create a graph

Returns
GGraph

A graph with the specified degree sequence. Nodes are labeled starting at 0 with an index corresponding to the position in the sequence.

Raises
NetworkXUnfeasible

If the degree sequence is not graphical.

NetworkXError

If a graph is not produced in specified number of tries

is_graphical, configuration_model

Notes

The generator algorithm [1] is not guaranteed to produce a graph.

References

1

Moshen Bayati, Jeong Han Kim, and Amin Saberi, A sequential algorithm for generating random graphs. Algorithmica, Volume 58, Number 4, 860-910, DOI: 10.1007/s00453-009-9340-1

Examples

>>> sequence = [1, 2, 2, 3]
>>> G = nx.random_degree_sequence_graph(sequence, seed=42)
>>> sorted(d for n, d in G.degree())
[1, 2, 2, 3]