Exact Solutions for Network Rewiring Models

TL;DR

This paper derives exact solutions for network rewiring models, providing a comprehensive mathematical framework applicable to various real-world evolving networks.

Contribution

It presents the full mean field equation for degree distribution and provides its exact and generating solutions, advancing the theoretical understanding of network rewiring.

Findings

Exact mean field equation for degree distribution derived

Analytical solutions for network rewiring models obtained

Applicable to diverse real-world network evolution processes

Abstract

Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.