A measure of betweenness centrality based on random walks

TL;DR

This paper introduces a new betweenness centrality measure based on random walks, capturing influence over information spread along all paths, not just shortest ones, with efficient matrix-based computation methods.

Contribution

It proposes a novel betweenness measure using random walks that considers all paths, relaxing the shortest-path assumption and enabling broader network influence analysis.

Findings

The new measure accounts for all paths, not just shortest ones.

Matrix methods allow efficient calculation of the measure.

Application examples demonstrate its practical utility.

Abstract

Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks.