Effective resistance on graphs and the Epidemic quasimetric

TL;DR

This paper introduces the epidemic quasimetric for graphs, compares it to existing metrics like effective resistance, and explores its applications in clustering and network analysis.

Contribution

The paper presents a new epidemic quasimetric on graphs and analyzes its properties relative to established metrics such as effective resistance and graph distance.

Findings

Epidemic quasimetric offers a novel perspective on graph clustering.

Comparison shows how epidemic quasimetric relates to effective resistance.

Potential applications in network analysis and clustering techniques.

Abstract

We introduce the epidemic quasimetric on graphs and study its behavior with respect to clustering techniques. In particular we compare its behavior to known objects such as the graph distance, effective resistance, and modulus of path families.