Fast counting of medium-sized rooted subgraphs
arXiv:1701.00177
Abstract
We prove that counting copies of any graph in another graph can be achieved using basic matrix operations on the adjacency matrix of . Moreover, the resulting algorithm is competitive for medium-sized : 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.
29 pages, 6 figures