Structure and dynamical behaviour of non-normal networks

TL;DR

This paper investigates the prevalence of non-normality in empirical networks across disciplines, revealing its impact on dynamics, stability, and noise sensitivity, and proposes models and metrics to analyze and generate non-normal networks.

Contribution

It identifies structural properties linked to non-normality, introduces models to generate such networks, and explores metrics for assessing their stability and dynamical behavior.

Findings

Non-normality is widespread in empirical networks.

Non-normal networks exhibit transient amplification of disturbances.

Metrics can effectively quantify non-normality and predict stability.

Abstract

We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. Additionally, eigenvalues may become extremely sensible to noise, and have a diminished physical meaning. We identify structural properties of networks that are associated to non-normality and propose simple models to generate networks with a tuneable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality, and propose their potential use in the context of the stability of complex ecosystems.