Emergence of bimodality in controlling complex networks

TL;DR

This paper introduces an analytical framework to classify nodes in complex networks, revealing two distinct control modes—centralized and distributed—and demonstrating how small structural changes can switch between these modes.

Contribution

It develops a novel method to categorize nodes in network control, uncovering bimodal control modes and their susceptibility to structural perturbations.

Findings

Identifies critical, intermittent, and redundant nodes in control configurations.

Predicts control modes for arbitrary networks.

Shows small structural changes can switch control modes.

Abstract

Our ability to control complex systems is a fundamental challenge of contemporary science. Recently introduced tools to identify the driver nodes, nodes through which we can achieve full control, predict the existence of multiple control configurations, prompting us to classify each node in a network based on their role in control. Accordingly a node is critical, intermittent or redundant if it acts as a driver node in all, some or none of the control configurations. Here we develop an analytical framework to identify the category of each node, leading to the discovery of two distinct control modes in complex systems: centralized vs distributed control. We predict the control mode for an arbitrary network and show that one can alter it through small structural perturbations. The uncovered bimodality has implications from network security to organizational research and offers new insights into the dynamics and control of complex systems.