Studying new classes of graph metrics

TL;DR

This paper explores new classes of graph metrics, such as path, reliability, walk, and logarithmic forest distances, highlighting their connections and potential applications in data analysis.

Contribution

It introduces and discusses several novel graph metrics based on cutpoint additive distances, expanding the toolkit beyond classical measures.

Findings

Identifies multiple new graph metrics including path, reliability, walk, and logarithmic forest distances.

Establishes connections between these new metrics and existing graph distances.

Provides insights into potential applications of these metrics in data analysis.

Abstract

In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them featuring the cutpoint additive distances. These include the path distances, the reliability distance, the walk distances, and the logarithmic forest distances among others. We discuss a number of connections between these and other distances.