Structural phase transition in evolving networks

Details Structural phase transition in evolving networks Structural phase transition in evolving networks

2009-05-10

arxiv.org/abs/0905.1470v1

Phys. Rev. E 80, 026119 (2009)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5figures

Scientific paper

10.1103/PhysRevE.80.026119

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.

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