Diffusion Processes on Power-Law Small-World Networks

TL;DR

This paper investigates diffusion processes on power-law small-world networks across various dimensions, revealing complex phase behavior and providing a unifying scaling framework for understanding such processes.

Contribution

It introduces a comprehensive analysis of diffusion on power-law small-world networks, including a detailed phase diagram and a scaling theory applicable to different link distributions.

Findings

Rich phase diagram with transient and recurrent phases

Critical line with varying exponents

Scaling theory for processes on small-world networks

Abstract

We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying exponents. The results were obtained using self-consistent perturbation theory and can also be understood in terms of a scaling theory, which provides a general framework for understanding processes on small-world networks with different distributions of long-range links.