An algorithm for counting short cycles in bipartite graphs

Authors:
T. R. Halford;K. M. Chugg
Affiliations:
Commun. Sci. Inst., Univ. of Southern California, Los Angeles, CA, USA;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

Let G=(U∪W, E) be a bipartite graph with disjoint vertex sets U and W, edge set E, and girth g. This correspondence presents an algorithm for counting the number of cycles of length g, g+2, and g+4 incident upon every vertex in U∪W. The proposed cycle counting algorithm consists of integer matrix operations and its complexity grows as O(gn3) where n=max(|U|,|W|).