Scale-Free Structure Emerging from Co-Evolution of a Network and the Concentration of Diffusive Resources on It

TL;DR

This paper presents a co-evolution model where resource diffusion and network structure influence each other, leading to the emergence of scale-free networks and dynamic node rankings, providing insights into real-world diffusion-driven systems.

Contribution

It introduces a simple, unified model of co-evolving networks with resource diffusion and link weight evolution, explaining the emergence of scale-free structures and dynamic rankings.

Findings

Networks develop scale-free properties asymptotically.

Dissipation leads to a dynamic scale-free phase with changing node rankings.

The model applies broadly to various real-world diffusion systems.

Abstract

Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of real-world network systems. We propose a simple model of such co-evolving network dynamics, in which the diffusion of a resource over a weighted network and the resource-driven evolution of the link weights occur simultaneously. We demonstrate that, under feasible conditions, the network robustly acquires scale-free characteristics in the asymptotic state. Interestingly, in the case that the system includes dissipation, it asymptotically realizes a dynamical phase characterized by an organized scale-free network, in which the ranking of each node with respect to the quantity of the resource possessed thereby changes ceaselessly. Our model offers a unified framework for understanding some real-world diffusion-driven network systems of diverse types.