Digraphs are different: Why directionality matters in complex systems

TL;DR

This paper explores how the directionality of edges in directed networks influences their topological properties and dynamical behavior, revealing that alignment with a global direction underpins phenomena like trophic coherence and non-normality.

Contribution

It uncovers the common origin of topological properties in directed networks and demonstrates their impact on dynamical behavior through simple models.

Findings

Directed network properties are linked to edge alignment with a global direction.

Alignment influences stability, percolation, and dynamical features.

Rich behaviors emerge even in simple models due to edge alignment effects.

Abstract

Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect stability, percolation and other dynamical features. I show here that these topological properties have a common origin, in that the edges of directed networks can be aligned - or not - with a global direction. And I illustrate how this can lead to rich and unexpected dynamical behaviour even in the simplest of models.