Influence and Influenceability: Global Directionality in Directed Complex Networks

TL;DR

This paper demonstrates that influence and influenceability in directed complex networks are fundamentally governed by the network's hierarchical structure and global directionality, as measured by trophic levels and coherence.

Contribution

It introduces the use of Trophic Analysis to connect global network properties with influence dynamics, revealing how hierarchy shapes influence and influenceability.

Findings

Trophic hierarchy explains influence reach and eigenvector centrality localization.

Global directionality mediates influence phenomena in directed networks.

Trophic coherence affects structural properties like pseudospectra in real networks.

Abstract

Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of Trophic Analysis to study directed networks and show that both "influence" and "influenceability" in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localises; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalised rock-paper-scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted, that node hierarchy is essential for understanding network influence, mediated by global directionality, are applicable to many real-world dynamics.