Exact Solutions for Network Rewiring Models

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.

7 pages, 7 figures. Minor changes and corrections made for publication

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• Wealth Condensation in Pareto Macro-Economies
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• Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition
• Exact Solutions for Models of Cultural Transmission and Network Rewiring
• Phase transition of social learning collectives and "Echo chamber"
• Spontaneous centralization of control in a network of company ownerships
• A generalized theory of preferential linking
• Network Rewiring Models
• Word statistics in Blogs and RSS feeds: Towards empirical universal evidence
• Are Copying and Innovation Enough?
• Neutral evolution and turnover over centuries of English word popularity