Random walk centrality in interconnected multilayer networks

TL;DR

This paper extends random walk betweenness and closeness centrality measures to interconnected multilayer networks using tensor formalism, providing analytical expressions validated by numerical results.

Contribution

It introduces a tensor-based framework to define and analyze centrality measures in multilayer networks, advancing understanding of node influence in complex interconnected systems.

Findings

Analytical expressions for centrality measures in multilayer networks

Validation of formulas through numerical experiments

Enhanced understanding of node influence in complex systems

Abstract

Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in many fields, from economics to biology and from urban planning to social sciences, to identify the most (or the less) influential nodes in a network using centrality measures. However, defining the centrality of actors in interconnected complex networks is not trivial. In this paper, we rely on the tensorial formalism recently proposed to characterize and investigate this kind of complex topologies, and extend two well known random walk centrality measures, the random walk betweenness and closeness centrality, to interconnected multilayer networks. For each of the measures we provide analytical expressions that completely agree with numerically results.