Classical and quantum random-walk centrality measures in multilayer networks

TL;DR

This paper introduces a framework for calculating classical and quantum random-walk centrality measures in multilayer networks, revealing differences and correlations between these measures through applications to synthetic and real-world networks.

Contribution

It formulates occupation, PageRank, betweenness, and closeness centralities for classical and quantum walks on multilayer networks, highlighting their differences and similarities.

Findings

Quantum centralities differ significantly from classical ones.

Certain random-walk centralities correlate with geodesic-path centralities.

Insights into the structural importance of nodes in multilayer networks.

Abstract

Multilayer network analysis is a useful approach for studying the structural properties of entities with diverse, multitudinous relations. Classifying the importance of nodes and node-layer tuples is an important aspect of the study of multilayer networks. To do this, it is common to calculate various centrality measures, which allow one to rank nodes and node-layers according to a variety of structural features. In this paper, we formulate occupation, PageRank, betweenness, and closeness centralities in terms of node-occupation properties of different types of continuous-time classical and quantum random walks on multilayer networks. We apply our framework to a variety of synthetic and real-world multilayer networks, and we identify marked differences between classical and quantum centrality measures. Our computations also give insights into the correlations between certain random-walk-based and geodesic-path-based centralities.