is_pseudographical#

is_pseudographical(sequence)[source]#

Returns True if some pseudograph can realize the sequence.

Every nonnegative integer sequence with an even sum is pseudographical (see [1]).

Parameters:

sequencelist or iterable container: A sequence of integer node degrees

Returns:

validbool: True if the sequence is a pseudographic degree sequence and False if not.

Notes

The worst-case run time is \(O(n)\) where n is the length of the sequence.

References

[1]

F. Boesch and F. Harary. “Line removal algorithms for graphs and their degree lists”, IEEE Trans. Circuits and Systems, CAS-23(12), pp. 778-782 (1976).

Examples

>>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (3, 4), (4, 2), (5, 1), (5, 4)])
>>> sequence = (d for _, d in G.degree())
>>> nx.is_pseudographical(sequence)
True

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