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arXiv · 0905.1470

Structural phase transition in evolving networks

Sang-Woo Kim·Jae Dong Noh
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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.

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BibTeXRIS

Sang-Woo Kim, Jae Dong Noh. 2009-05-10. Structural phase transition in evolving networks. https://doi.org/10.1103/physreve.80.026119

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