Modulus metrics on networks

Abstract

The concept of p-modulus gives a way to measure the richness of a family of objects on a graph. In this paper, we investigate the families of con-necting walks between two fixed nodes and show how to use p-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 antisnowaking 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.