Modulus metrics on networks
Nathan Albin, Nethali Fernando, Pietro Poggi‐Corradini · Discrete and Continuous Dynamical Systems - B · 2018
The concept of \begin{document}$p$\end{document} -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 \begin{document}$p$\end{document} -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.