Analytic description of adaptive network topologies in steady state

TL;DR

This paper derives approximate degree distributions for adaptive networks in steady state, explaining their properties and showing good agreement with simulations, with potential for broader application to coevolutionary dynamics.

Contribution

It provides a novel analytical approach to describe the topology of adaptive networks in steady state, extending understanding of coevolutionary systems.

Findings

Degree distributions match simulations well in most cases.

Rewiring speed affects the accuracy of the approximation.

Method generalizes to other coevolutionary dynamics.

Abstract

In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in such active steady states. These distributions are shown to agree quantitatively with simulations except when rewiring is much faster than state update, and used to predict and to explain general properties of steady-state topologies. The method generalizes easily to other coevolutionary dynamics.