2016/12/31 by Maugis, P-A. G., Olhede, S. C., Wolfe, P. J.
#05C50 #68Q25 #68R10 #90C35 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Social and Information Networks (cs.SI)
paper · doi:10.48550/arxiv.1701.00177
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.