is_graphical

is_graphical(sequence, method='eg')

Returns True if sequence is a valid degree sequence.

A degree sequence is valid if some graph can realize it.

Parameters:

sequencelist or iterable container

A sequence of integer node degrees

method“eg” | “hh” (default: ‘eg’)

The method used to validate the degree sequence. “eg” corresponds to the Erdős-Gallai algorithm [EG1960], [choudum1986], and “hh” to the Havel-Hakimi algorithm [havel1955], [hakimi1962], [CL1996].

Returns:

validbool

True if the sequence is a valid degree sequence and False if not.

References

[EG1960]

Erdős and Gallai, Mat. Lapok 11 264, 1960.

[choudum1986]

S.A. Choudum. “A simple proof of the Erdős-Gallai theorem on graph sequences.” Bulletin of the Australian Mathematical Society, 33, pp 67-70, 1986. https://doi.org/10.1017/S0004972700002872

[havel1955]

Havel, V. “A Remark on the Existence of Finite Graphs” Casopis Pest. Mat. 80, 477-480, 1955.

[hakimi1962]

Hakimi, S. “On the Realizability of a Set of Integers as Degrees of the Vertices of a Graph.” SIAM J. Appl. Math. 10, 496-506, 1962.

[CL1996]

G. Chartrand and L. Lesniak, “Graphs and Digraphs”, Chapman and Hall/CRC, 1996.

Examples

>>> G = nx.path_graph(4)
>>> sequence = (d for n, d in G.degree())
>>> nx.is_graphical(sequence)
True

To test a non-graphical sequence: >>> sequence_list = [d for n, d in G.degree()] >>> sequence_list[-1] += 1 >>> nx.is_graphical(sequence_list) False