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

Return 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 :

sequence : list of integers

Sequence of degrees

seed : hashable object, optional

Seed for random number generator

tries : int, optional

Maximum number of tries to create a graph

Returns :

G : Graph

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

Raises :


If the degree sequence is not graphical.


If a graph is not produced in specified number of tries

See also

is_valid_degree_sequence, configuration_model


The generator algorithm [R284] is not guaranteed to produce a graph.


[R284](1, 2) 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


>>> sequence = [1, 2, 2, 3]
>>> G = nx.random_degree_sequence_graph(sequence)
>>> sorted(G.degree().values())
[1, 2, 2, 3]