Maximal-entropy random walk unifies centrality measures

TL;DR

This paper explores the connections between different centrality measures in complex networks, emphasizing the unique properties of the maximal-entropy random walk and its impact on network analysis.

Contribution

It introduces a unified framework linking various centrality measures through analogies between similarity matrices and highlights the distinctiveness of the maximal-entropy random walk in network analysis.

Findings

Maximal-entropy random walk centralities form a distinct cluster.

Centralities based on maximal-entropy random walk align closely with eigenvector centrality.

Different random walk-based centralities group into two separate families.

Abstract

In this paper analogies between different (dis)similarity matrices are derived. These matrices, which are connected to path enumeration and random walks, are used in community detection methods or in computation of centrality measures for complex networks. The focus is on a number of known centrality measures, which inherit the connections established for similarity matrices. These measures are based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the stationary state, stochastic matrix or mean first-passage times of a random walk. Particular attention is paid to the maximal-entropy random walk, which serves as a very distinct alternative to the ordinary random walk used in network analysis. The various importance measures, defined both with the use of ordinary random walk and the maximal-entropy random walk, are compared numerically on a set of benchmark graphs. It is shown that groups of centrality measures defined with the two random walks cluster into two separate families. In particular, the group of centralities for the maximal-entropy random walk, connected to the eigenvector centrality and path enumeration, is strongly distinct from all the other measures and produces largely equivalent results.