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

See also

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]