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is_digraphical

is_digraphical(in_sequence, out_sequence)[source]

Returns True if some directed graph can realize the in- and out-degree sequences.

Parameters:
  • in_sequence (list or iterable container) – A sequence of integer node in-degrees
  • out_sequence (list or iterable container) – A sequence of integer node out-degrees
Returns:

valid – True if in and out-sequences are digraphic False if not.
Return type:

bool

Notes

This algorithm is from Kleitman and Wang [1]. The worst case runtime is O(s * log n) where s and n are the sum and length of the sequences respectively.

References

[1]D.J. Kleitman and D.L. Wang Algorithms for Constructing Graphs and Digraphs with Given Valences and Factors, Discrete Mathematics, 6(1), pp. 79-88 (1973)