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

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Johnson, Samuel
Torres, Joaquin J.
Marro, Joaquin
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Abstract
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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.
Keywords
Nonlinear Sciences - Adaptation and Self-Organizing Systems, Condensed Matter - Statistical Mechanics
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