The diminishing role of hubs in dynamical processes on complex networks

TL;DR

This paper introduces information-theoretical methods to analyze the influence of individual units in complex networks, revealing that highly connected hubs have less impact on dynamics than intermediate nodes, challenging traditional assumptions.

Contribution

It develops novel analytical tools to quantify node contributions in complex systems and demonstrates that hubs are less influential on system dynamics than previously thought.

Findings

Highly connected units have less impact than intermediate ones.

Hubs influence long-term behavior but have short-lived effects on system trajectories.

Empirical evidence from social, biological, and neural networks supports the findings.

Abstract

It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics as compared to intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein-protein interaction network, and a neural network, suggesting that it might indeed be a widespread property in nature.