Modulus on graphs as a generalization of standard graph theoretic quantities
Combinatorics
2021-02-09 v2 Optimization and Control
Abstract
This paper presents new results for the modulus of families of walks on a graph---a discrete analog of the modulus of curve families due to Beurling and Ahlfors. Particular attention is paid to the dependence of the modulus on its parameters. Modulus is shown to generalize (and interpolate among) three important quantities in graph theory: shortest path, effective resistance, and max-flow or min-cut.
Keywords
Cite
@article{arxiv.1504.02418,
title = {Modulus on graphs as a generalization of standard graph theoretic quantities},
author = {Nathan Albin and Megan Brunner and Roberto Perez and Pietro Poggi-Corradini and Natalie Wiens},
journal= {arXiv preprint arXiv:1504.02418},
year = {2021}
}
Comments
Updated with referee's comments. To appear in ECGD