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havel_hakimi_graph(deg_sequence, create_using=None)[source]

Return a simple graph with given degree sequence constructed using the Havel-Hakimi algorithm.

Parameters :

deg_sequence: list of integers

Each integer corresponds to the degree of a node (need not be sorted).

create_using : graph, optional (default Graph)

Return graph of this type. The instance will be cleared. Directed graphs are not allowed.

Raises :


For a non-graphical degree sequence (i.e. one not realizable by some simple graph).


The Havel-Hakimi algorithm constructs a simple graph by successively connecting the node of highest degree to other nodes of highest degree, resorting remaining nodes by degree, and repeating the process. The resulting graph has a high degree-associativity. Nodes are labeled 1,.., len(deg_sequence), corresponding to their position in deg_sequence.

The basic algorithm is from Hakimi [R282] and was generalized by Kleitman and Wang [R283].


[R282](1, 2) Hakimi S., On Realizability of a Set of Integers as Degrees of the Vertices of a Linear Graph. I, Journal of SIAM, 10(3), pp. 496-506 (1962)
[R283](1, 2) Kleitman D.J. and Wang D.L. Algorithms for Constructing Graphs and Digraphs with Given Valences and Factors Discrete Mathematics, 6(1), pp. 79-88 (1973)