Bringing order to network centrality measures

TL;DR

This paper presents a new quantitative method for comparing different graph centrality measures based on vertex ordering, enabling formal analysis, approximation, and exploration of conjectures in network analysis.

Contribution

It introduces a simple, elegant framework for comparing centrality measures and formalizes conjectures, facilitating new insights and approximation schemes in network science.

Findings

A new method for comparing centrality measures based on vertex ordering

Formalization of existing conjectures in network analysis

Development of an approximation scheme for practical use

Abstract

We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative restatement of many conjectures that were previously cumbersome to formalize. Moreover, it produces an approximation scheme useful for network scientists. We explore some of these uses and formulate new conjectures that are of independent interest.