Unified model for network dynamics exhibiting nonextensive statistics

TL;DR

This paper presents a unified dynamical network model that captures various known network behaviors, including static, growing, and rewiring networks, all exhibiting q-exponential degree distributions and related nonextensive statistical properties.

Contribution

It introduces a comprehensive model that unifies different network dynamics and demonstrates their common nonextensive statistical features, expanding understanding of complex network behaviors.

Findings

Networks exhibit q-exponential degree distributions across parameters.

Model encompasses static, growing, and rewiring networks.

Clustering coefficients and connectivity distributions depend on parameters.

Abstract

We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing networks, preferentially growing networks, and (preferentially) rewiring networks. Further, it exhibits a natural random graph limit. The proposed model generalizes network dynamics to rewiring and growth modes which depend on internal topology as well as on a metric imposed by the space they are embedded in. In all of the networks emerging from the presented model we find q-exponential degree distributions over a large parameter space. We comment on the parameter dependence of the corresponding entropic index q for the degree distributions, and on the behavior of the clustering coefficients and neighboring connectivity distributions.