Levy 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 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.

arXiv comment11 pages and 6 figures

References in corpus (23)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Synchronization in complex networks
• Critical phenomena in complex networks
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• The Dynamics of Viral Marketing
• Diffusion dynamics on multiplex networks
• Structural measures for multiplex networks
• Explosive Synchronization Transitions in Scale-free Networks
• Random Walks on Multiplex Networks
• Abrupt transition in the structural formation of interconnected networks
• Contact-based Social Contagion in Multiplex Networks
• Assortativity Decreases the Robustness of Interdependent Networks
• Effect of the Interconnected Network Structure on the Epidemic Threshold
• Random walks and search in time-varying networks
• Designing optimal transport networks
• Explosive percolation in scale-free networks
• Random walks on weighted networks
• Long-Range Navigation on Complex Networks using Lévy Random Walks
• Dimensionality reduction and spectral properties of multilayer networks
• From the Physics of Interacting Polymers to Optimizing Routes on the London Underground
• Random walks in modular scale-free networks with multiple traps
• Random Walks on Complex Networks