Structure and dynamical behaviour of non-normal networks

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.