Diffusive behavior of multiplex networks

Abstract: Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time scale of the multiplex to reach equilibrium is smaller than that of single networks in isolation, can emerge due to the interplay of these two mechanisms. In the limits of strong and weak inter-layer couplings multiplex diffusion has been linked to the spectrum of the supra-Laplacian associated to the system. However, a general theory for the emergence of this behavior is still lacking. Here we shed light on how the structural and dynamical features of the multiplex affect the Laplacian spectral properties. For instance, we find that super-diffusion emerges the earliest in systems with poorly diffusive layers, and that its onset is independent from the presence of overlap, which only influences the maximum relative intensity of the phenomenon. Moreover, a uniform allocation of resources to enhance diffusion within layers is preferable, as highly intra-layer heterogenous flows might hamper super-diffusion. Last, in multiplex networks formed by many layers, diffusion is best promoted by strengthening inter-layer flows across dissimilar layers. Our work can turn useful for the design of interconnected infrastructures in real-world transportation systems, clarifying the determinants able to drive the system towards the super-diffusive regime.