Levy random walks on multiplex networks

TL;DR

This paper investigates Levy random walks on multiplex networks, deriving analytical expressions for navigation efficiency and demonstrating their potential advantages over other strategies in complex, layered network structures.

Contribution

It introduces a novel Levy random walk model on multiplex networks and provides analytical tools to evaluate its efficiency, highlighting its advantages over existing methods.

Findings

Levy random walks can outperform other strategies in certain multiplex network conditions.

Analytical expressions for mean first passage time on multiplex networks are derived.

Levy walks' efficiency depends on network structure and parameters.

Abstract

Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes that occur on top of them. Here, inspired by one specific model of random walks that seems to be ubiquitous across many scientific fields, the Levy flight, we study a new navigation strategy on top of multiplex networks. Capitalizing on spectral graph and stochastic matrix theories, we derive analytical expressions for the mean first passage time and the average time to reach a node on these networks. Moreover, we also explore the efficiency of Levy random walks, which we found to be very different as compared to the single layer scenario, accounting for the structure and dynamics inherent to the multiplex network. Finally, by comparing with some other important random walk processes defined on multiplex networks, we find that in some region of the parameters, a Levy random walk is the most efficient strategy. Our results give us a deeper understanding of Levy random walks and show the importance of considering the topological structure of multiplex networks when trying to find efficient navigation strategies.