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arXiv · 1701.00177

Fast counting of medium-sized rooted subgraphs

P-A. G. Maugis·S. C. Olhede·P. J. Wolfe
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Abstract

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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P-A. G. Maugis, S. C. Olhede, P. J. Wolfe. 2017-01-13. Fast counting of medium-sized rooted subgraphs. https://arxiv.org/abs/1701.00177

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