Diffusion-annihilation proecesses in weighted scale-free networks with identical degree sequence

TL;DR

This paper investigates diffusion-annihilation processes on weighted scale-free networks with identical degree sequences, revealing that disassortative mixing and weight-degree correlation significantly influence particle segregation and depletion zones.

Contribution

It demonstrates that disassortative mixing and weight-degree correlation, not just degree distribution, are key factors affecting diffusion-annihilation dynamics on these networks.

Findings

Disassortative mixing causes particle segregation.

Weight-degree correlation influences process dynamics.

Degree distribution alone does not characterize the processes.

Abstract

The studies based on $A+A \rightarrow \emptyset$ and $A+B\rightarrow \emptyset$ diffusion-annihilation processes have so far been studied on weighted uncorrelated scale-free networks and fractal scale-free networks. In the previous reports, it is widely accepted that the segregation of particles in the processes is introduced by the fractal structure. In this paper, we study these processes on a family of weighted scale-free networks with identical degree sequence. We find that the depletion zone and segregation are essentially caused by the disassortative mixing, namely, high-degree nodes tend to connect with low-degree nodes. Their influence on the processes is governed by the correlation between the weight and degree. Our finding suggests both the weight and degree distribution don't suffice to characterize the diffusion-annihilation processes on weighted scale-free networks.