Structural phase transition in evolving networks

TL;DR

This paper introduces a coupled network-particle model demonstrating a phase transition from homogeneous to hub-dominated structures driven by feedback between traffic and network evolution.

Contribution

It presents a novel model where network structure co-evolves with diffusing particles, revealing a phase transition mechanism for hub formation.

Findings

The model exhibits a phase transition between homogeneous and heterogeneous network phases.

Hubs emerge due to positive feedback between particle diffusion and edge weight dynamics.

The transition is characterized by a shift from exponential degree distribution to hub dominance.

Abstract

A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model consists of an undirected weighted network of fixed mean degree and randomly diffusing particles of fixed density. The weight $w$ of an edge increases by the amount of traffics through its connecting nodes or decreases by a constant factor. Edges are removed with the probability $P_{rew.}=1/(1+w)$ and replaced by new ones having $w=0$ at random locations. We find that the model exhibits a structural phase transition between the homogeneous phase characterized by an exponentially decaying degree distribution and the heterogeneous phase characterized by the presence of hubs. The hubs emerge as a consequence of a positive feedback between the particle and the edge dynamics.