networkx.algorithms.graphical.is_valid_degree_sequence_havel_hakimi¶
-
is_valid_degree_sequence_havel_hakimi
(deg_sequence)[source]¶ Returns True if deg_sequence can be realized by a simple graph.
The validation proceeds using the Havel-Hakimi theorem. Worst-case run time is \(O(s)\) where \(s\) is the sum of the sequence.
Parameters: deg_sequence (list) – A list of integers where each element specifies the degree of a node in a graph. Returns: valid – True if deg_sequence is graphical and False if not. Return type: bool Notes
The ZZ condition says that for the sequence d if
\[|d| >= \frac{(\max(d) + \min(d) + 1)^2}{4*\min(d)}\]then d is graphical. This was shown in Theorem 6 in [1].
References
[1] I.E. Zverovich and V.E. Zverovich. “Contributions to the theory of graphic sequences”, Discrete Mathematics, 105, pp. 292-303 (1992).