Structural phase transition in evolving networks

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.