English

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 FF in another graph GG can be achieved using basic matrix operations on the adjacency matrix of GG. Moreover, the resulting algorithm is competitive for medium-sized FF: 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.

Keywords

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

R2 v1 2026-06-22T17:38:34.100Z