A dynamical characterization of the small world phase

TL;DR

This paper introduces a dynamical method using coupled map systems to characterize the small-world phase in networks, linking phase transitions to ergodic invariants, offering a new perspective beyond traditional topological measures.

Contribution

It presents a novel dynamical approach to identify the small-world phase, connecting network properties with ergodic invariants of coupled map dynamics.

Findings

Entrance and exit from the SW phase are related to ergodic invariants.

The dynamical approach provides a new way to characterize small-world networks.

Traditional topological coefficients are complemented by dynamical analysis.

Abstract

Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these networks. Here a dynamical approach is used to characterize the small-world phenomenon. Using the $\beta -$model, a coupled map dynamical system is defined on the network. Entrance to and exit from the SW phase are related to the behavior of the ergodic invariants of the dynamics.