Sensitivity of Complex Networks

TL;DR

This paper develops a framework to quantify the sensitivity of complex networks, revealing that power-law architectures with hubs exhibit unique dynamic responses and critical frequency behaviors.

Contribution

It introduces necessary and sufficient conditions for emergent macroscopic dynamics in large networks, highlighting the role of power-law degree distributions.

Findings

Power-law networks satisfy conditions for new dynamic behaviors.

Hubs influence sensitivity only up to a critical frequency.

Sensitivity depends on network architecture and node connectivity.

Abstract

The sensitivity (i.e. dynamic response) of complex networked systems has not been well understood, making difficult to predict whether new macroscopic dynamic behavior will emerge even if we know exactly how individual nodes behave and how they are coupled. Here we build a framework to quantify the sensitivity of complex networked system of coupled dynamic units. We characterize necessary and sufficient conditions for the emergence of new macroscopic dynamic behavior in the thermodynamic limit. We prove that these conditions are satisfied only for architectures with power-law degree distributions. Surprisingly, we find that highly connected nodes (i.e. hubs) only dominate the sensitivity of the network up to certain critical frequency.