Dynamic rewiring in small world networks

TL;DR

This paper studies the equilibrium properties of small world networks with dynamic connectivity and spins, revealing a Poisson-like degree distribution and validating findings with simulations.

Contribution

It introduces a method to analyze equilibrium in dynamic small world networks using replicated transfer matrices and population dynamics.

Findings

Degree distribution is Poisson-like in equilibrium.

Results are confirmed by Glauber simulations.

Both spin and graph statistics are analyzed at equilibrium.

Abstract

We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us to examine order parameters of our system at total equilibrium, probing both spin- and graph-statistics. Of these, interestingly, the degree distribution is found to acquire a Poisson-like form (both within and outside the ordered phase). Comparison with Glauber simulations confirms our results satisfactorily.