Priority diffusion model in lattices and complex networks

TL;DR

This paper introduces a priority-based diffusion model for particles in lattices and complex networks, revealing how priority affects diffusion rates and causes trapping in heterogeneous networks, especially scale-free ones.

Contribution

The paper presents a novel diffusion model with priority rules and analytically characterizes how these rules influence particle mobility and trapping in different network topologies.

Findings

Diffusion of high-priority particles is normal in lattices.

Low-priority particles diffuse slower and can become trapped in scale-free networks.

The fraction of free sites for low-priority particles decreases exponentially with node degree.

Abstract

We introduce a model for diffusion of two classes of particles ($A$ and $B$) with priority: where both species are present in the same site the motion of $A$'s takes precedence over that of $B$'s. This describes realistic situations in wireless and communication networks. In regular lattices the diffusion of the two species is normal but the $B$ particles are significantly slower, due to the presence of the $A$ particles. From the fraction of sites where the $B$ particles can move freely, which we compute analytically, we derive the diffusion coefficients of the two species. In heterogeneous networks the fraction of sites where $B$ is free decreases exponentially with the degree of the sites. This, coupled with accumulation of particles in high-degree nodes leads to trapping of the low priority particles in scale-free networks.