Nonlinear preferential rewiring in fixedsize networks as a diffusion process
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 powerlaw kernels with exponents α and β , the stationary states which the degree distributions evolve toward exhibit a secondorder phase transition—from relatively homogeneous to highly heterogeneous (with the emergence of starlike structures) at α=β . 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 α and 1α .
 Publication:

Physical Review E
 Pub Date:
 May 2009
 DOI:
 10.1103/PhysRevE.79.050104
 arXiv:
 arXiv:0905.1666
 Bibcode:
 2009PhRvE..79e0104J
 Keywords:

 64.60.aq;
 05.10.a;
 05.40.a;
 89.75.k;
 Networks;
 Computational methods in statistical physics and nonlinear dynamics;
 Fluctuation phenomena random processes noise and Brownian motion;
 Complex systems;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Physical Review E 79, 050104(R) (2009)