A Topological Mechanism of Superdiffusion on Duplex Networks

Superdiffusion is an interesting phenomenon from both theoretical and practical perspectives. In this article, we propose a sufficient condition for the occurrence of superdiffusion on duplex networks by applying the generating functionology from combinatorial mathematics. Our result indicates that, with fixed values of intralayer diffusion constants, superdiffusion emerges from a certain combination of different network topologies, which provides a topological mechanism to regulate the whole diffusion process. On a more general ground, we provide two interlayer linking strategies to expand the applicability of the aforementioned topological mechanism on real-world networks, and construct a class of specific duplex networks on which superdiffusion occurs. We further verify that diffusion with negative interlayer correlation is faster than that with positive correlation from a typical duplex structure. Given the ubiquity of diffusion in the real world, our results constitute a significant step toward a better understanding of superdiffusion processes on multiplex networks.