Nonlinear preferential rewiring in fixed-size networks as a diffusion process
Adaptation and Self-Organizing Systems
2010-01-27 v1 Statistical Mechanics
Abstract
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.
Cite
@article{arxiv.0905.1666,
title = {Nonlinear preferential rewiring in fixed-size networks as a diffusion process},
author = {Samuel Johnson and Joaquin J. Torres and Joaquin Marro},
journal= {arXiv preprint arXiv:0905.1666},
year = {2010}
}