Universality of non-normality in real complex networks

Network theory has been a groundbreaking research field in science for the last 20 years, conceivably the only one that could glue together disparate and even contrasting disciplines such as physics, economy, biology or sociology. A network materialises the complex interactions between the composing entities of large systems, it thus defines the natural and structural backbone for describing complex systems, which dynamics is unavoidably bound to the network properties. Based on a detailed study involving a large set of empirical networks arising from a wide spectrum of research fields, we claim that strong non-normality is indeed a universal property in network science [1].
Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, initial small disturbances can undergo a transient phase and be strongly amplified although the system is linearly stable [2]. We hence propose several models to generate complex non-normal networks to explain the origin of such property. Because of the non-normality of the networked support, the comprehension of the dynamical properties goes beyond the classical linear spectral methods, while we show that the pseudo- spectrum is able to capture such behaviour. This response is very general and it challenges our understanding of natural processes grounded in real networks, as we illustrate in the Generalised Lotka-Volterra model.