Two betweenness centrality measures based on Randomized Shortest Paths

TL;DR

This paper proposes two novel betweenness centrality measures based on the Randomized Shortest Paths framework, which effectively balance shortest path and random walk approaches to better identify important nodes in networks.

Contribution

It introduces new RSP-based betweenness centralities that combine shortest and random path ideas, with efficient computation methods and demonstrated real-world utility.

Findings

Effective identification of important network nodes.

Balances shortest path and random walk analyses.

Shows advantages over traditional centrality measures.

Abstract

This paper introduces two new closely related betweenness centrality measures based on the Randomized Shortest Paths (RSP) framework, which fill a gap between traditional network centrality measures based on shortest paths and more recent methods considering random walks or current flows. The framework defines Boltzmann probability distributions over paths of the network which focus on the shortest paths, but also take into account longer paths depending on an inverse temperature parameter. RSP's have previously proven to be useful in defining distance measures on networks. In this work we study their utility in quantifying the importance of the nodes of a network. The proposed RSP betweenness centralities combine, in an optimal way, the ideas of using the shortest and purely random paths for analysing the roles of network nodes, avoiding issues involving these two paradigms. We present the derivations of these measures and how they can be computed in an efficient way. In addition, we show with real world examples the potential of the RSP betweenness centralities in identifying interesting nodes of a network that more traditional methods might fail to notice.