Fast counting of medium-sized rooted subgraphs
Discrete Mathematics
2017-01-16 v2 Social and Information Networks
Combinatorics
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.
Cite
@article{arxiv.1701.00177,
title = {Fast counting of medium-sized rooted subgraphs},
author = {P-A. G. Maugis and S. C. Olhede and P. J. Wolfe},
journal= {arXiv preprint arXiv:1701.00177},
year = {2017}
}
Comments
29 pages, 6 figures