An algorithm for counting short cycles in bipartite graphs

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|).