Exact Solution for the Time Evolution of Network Rewiring Models

Details Exact Solution for the Time Evolution of Network Rewiring Models Exact Solution for the Time Evolution of Network Rewiring Models

2006-12-08

arxiv.org/abs/cond-mat/0612214v2

Phys.Rev.E. 75 (2007) 056101

Physics

Condensed Matter

Statistical Mechanics

This version contains a few footnotes not in published Phys.Rev.E version

Scientific paper

10.1103/PhysRevE.75.056101

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature including examples of Urn, Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a Minority game also show features described by our model.

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