Axiomatic Analysis of Medial Centrality Measures

TL;DR

This paper provides the first axiomatic analysis of medial centrality measures, including betweenness, stress, and random walk betweenness, revealing their foundational properties and relationships.

Contribution

It introduces axiomatic characterizations for three medial centrality measures, enhancing understanding of their theoretical foundations.

Findings

Random Walk Betweenness shares properties with classic measures

Axiomatic characterizations clarify measure differences and similarities

Analysis bridges shortest-path and random-walk centrality concepts

Abstract

We perform the first axiomatic analysis of medial centrality measures. These measures, also called betweenness-like centralities, assess the role of a node in connecting others in the network. We focus on a setting with one target node and several source nodes. We consider three classic medial centrality measures adapted to this setting: Betweenness Centrality, Stress Centrality and Random Walk Betweenness Centrality. While Betweenness and Stress Centralities assume that the information in the network follows shortest paths, Random Walk Betweenness Centrality assumes it moves randomly along the edges. We develop the first axiomatic characterizations of all three measures. Our analysis shows that Random Walk Betweenness, while conceptually different, shares several common properties with classic Betweenness and Stress Centralities.