An elementary proof of a matrix tree theorem for directed graphs
Combinatorics
2019-04-30 v1
Abstract
We present an elementary proof of a generalization of Kirchoff's matrix tree theorem to directed, weighted graphs. The proof is based on a specific factorization of the Laplacian matrices associated to the graphs, which only involves the two incidence matrices that capture the graph's topology. We also point out how this result can be used to calculate principal eigenvectors of the Laplacian matrices.
Keywords
Cite
@article{arxiv.1904.12221,
title = {An elementary proof of a matrix tree theorem for directed graphs},
author = {Patrick De Leenheer},
journal= {arXiv preprint arXiv:1904.12221},
year = {2019}
}
Comments
12 pages, 3 figures