title: Lévy random walks on multiplex networks.
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 Lévy 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 Lévy 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 Lévy random walk is the most efficient strategy. Our results give us a deeper understanding of Lévy random walks and show the importance of considering the topological structure of multiplex networks when trying to find efficient navigation strategies.
authors.affiliation: School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.|Key Laboratory of Mathematics Informatics Behavioral Semantics(LMIB), Ministry of Education, China.|Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50018, Spain.
authors.forename: Quantong
authors.initials: Q
authors.lastname: Guo
authors.affiliation: Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50018, Spain.
authors.forename: Emanuele
authors.initials: E
authors.lastname: Cozzo
authors.affiliation: School of Mathematics and Systems Science, Beihang University, Beijing 100191, China.|Key Laboratory of Mathematics Informatics Behavioral Semantics(LMIB), Ministry of Education, China.|School of Mathematical Sciences, Peking University, Beijing 100191, China.
authors.forename: Zhiming
authors.initials: Z
authors.lastname: Zheng
authors.affiliation: Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50018, Spain.|Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain.|Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Turin, Italy.
authors.forename: Yamir
authors.initials: Y
authors.lastname: Moreno