Strong Connectivity in Real Directed Networks

TL;DR

This paper demonstrates that strong connectivity in real directed networks is primarily influenced by hierarchical structure, and small targeted edge removals can significantly alter network dynamics.

Contribution

It introduces the concept of trophic coherence as a key factor in strong connectivity and provides a percolation-based framework to analyze the transition between connectivity regimes.

Findings

Strong connectivity depends on trophic coherence and hierarchy.

Critical point for connectivity transition identified via percolation theory.

Targeted edge removal can drastically change network dynamics.

Abstract

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behaviour of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering -- a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes, and confirm our results on many real-world networks, including ecological, neural, trade and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. And we illustrate with example dynamics -- the SIS model, majority vote, Kuramoto oscillators and the voter model -- how a small number of edge deletions can utterly change dynamical processes in a wide range of systems.