Nonlinear preferential rewiring in fixed-size 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 power-law kernels with exponents α and β , the stationary states which the degree distributions evolve toward exhibit a second-order 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 1-α .
- 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 Self-Organizing Systems;
- Condensed Matter - Statistical Mechanics
- E-Print:
- Physical Review E 79, 050104(R) (2009)