Nonlinear preferential rewiring in fixed-size networks as a diffusion process

Details Nonlinear preferential rewiring in fixed-size networks as a diffusion process Nonlinear preferential rewiring in fixed-size networks as a diffusion process

2009-05-11

arxiv.org/abs/0905.1666v1

Physical Review E 79, 050104(R) (2009)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

10.1103/PhysRevE.79.050104

We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with exponents alpha and beta, the stationary states the degree distributions evolve towards exhibit a second order phase transition - from relatively homogeneous to highly heterogeneous (with the emergence of starlike structures) at alpha = beta. Temporal evolution of the distribution in this critical regime is shown to follow a nonlinear diffusion equation, arriving at either pure or mixed power-laws, of exponents -alpha and 1-alpha.

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