Growing Networks with Enhanced Resilience to Perturbation

TL;DR

This paper introduces a novel mechanism for constructing scale-free networks based on the stability of dynamical systems, linking network topology to system resilience.

Contribution

It proposes a new model that connects scale-free network formation to the stability of systems, extending to weighted directed networks with power-law link strength distributions.

Findings

Power-law behavior observed in weighted network link strengths.

Scale-free networks linked to stability properties of dynamical systems.

Model applicable to diverse contexts due to universality.

Abstract

Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In this letter we propose a new mechanism for the construction of SF networks: Evolving networks as interaction networks of systems which are distinguished by their stability if perturbed out of equilibrium. Stability is measured by the largest real part of any eigenvalue of a matrix associated with the graph. We extend the model to weighted directed networks and report power law behaviour of the link strength distribution of the weighted graphs in the SF regime. The model we propose for the first time relates SF networks to stability properties of the underlying dynamical system.