Papers › Fast counting of medium-sized rooted subgraphs
Fast counting of medium-sized rooted subgraphs
P-A. G. Maugis, S. C. Olhede, P. J. Wolfe
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We prove that counting copies of any graph F in another graph G can be achieved using basic matrix operations on the adjacency matrix of G. Moreover, the resulting algorithm is competitive for medium-sized F: our algorithm recovers the best known complexity for rooted 6-clique counting and improves on the best known for 9-cycle counting. Underpinning our proofs is the new result that, for a general class of graph operators, matrix operations are homomorphisms for operations on rooted graphs.
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