An algorithm for counting short cycles in bipartite graphs

Let G=(U/spl cup/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/spl cup/W. The proposed cycle counting algorithm consists of i...

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Veröffentlicht in:	IEEE transactions on information theory 2006-01, Vol.52 (1), p.287-292
Hauptverfasser:	Halford, T.R., Chugg, K.M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Applied sciences Bipartite graph Bipartite graphs Coding, codes Complexity Concatenated codes Convolutional codes Counting cycles Decoding Exact sciences and technology girth Graph theory Graphical models graphical models of codes Graphs Information theory Information, signal and communications theory Integers Joining processes loops Mathematical models Parity check codes Signal and communications theory Telecommunications and information theory Vertex sets
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Beschreibung
Zusammenfassung:	Let G=(U/spl cup/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/spl cup/W. The proposed cycle counting algorithm consists of integer matrix operations and its complexity grows as O(gn/sup 3/) where n=max(\|U\|,\|W\|).
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2005.860472