Modulus metrics on networks
Metric Geometry
2021-02-09 v1
Abstract
The concept of -modulus gives a way to measure the richness of a family of objects on a graph. In this paper, we investigate the families of connecting walks between two fixed nodes and show how to use -modulus to form a parametrized family of graph metrics that generalize several well-known and widely-used metrics. We also investigate a characteristic of metrics called the "antisnowflaking exponent" and present some numerical findings supporting a conjecture about the new metrics. We end with explicit computations of the new metrics on some selected graphs.
Cite
@article{arxiv.1803.03680,
title = {Modulus metrics on networks},
author = {Nathan Albin and Nethali Fernando and Pietro Poggi-Corradini},
journal= {arXiv preprint arXiv:1803.03680},
year = {2021}
}
Comments
To appear in Discrete and Continuous Dynamical Systems - B