Connecting complex networks to nonadditive entropies

TL;DR

This paper demonstrates that scale-invariant networks can be modeled using nonadditive $q$-entropies, linking complex network behavior with generalized thermostatistics, and showing a correspondence with thermal problems.

Contribution

It establishes a connection between scale-invariant networks and nonadditive $q$-entropies, extending the applicability of generalized thermostatistics to complex networks.

Findings

Scale-invariant networks fit within the nonadditive entropy framework.

Numerical results suggest a correspondence with generalized thermal problems.

The $q$-generalized exponential replaces the Boltzmann-Gibbs exponential in these systems.

Abstract

Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving strong space-time entanglement. Its generalization based on nonadditive $q$-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a $d$-dimensional geographically located network with weighted links and exhibit its 'energy' distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann-Gibbs exponential factor is generically substituted by its $q$-generalisation, and is recovered in the $q=1$ limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.