Fundamental building blocks of controlling complex networks: A universal controllability framework

TL;DR

This paper introduces a universal framework for understanding the fundamental building blocks of controllability in complex networks, revealing how network topology influences control and identifying phase transitions in control properties.

Contribution

It develops a local-information-based dissection method to identify the origin of control roles of nodes and links, advancing the understanding of strong structural controllability.

Findings

Technological networks are more strongly structurally controllable than social and biological networks.

Real-world networks exhibit higher SSC than random networks, indicating resilience and adaptability.

The framework uncovers phase-transition phenomena related to network control properties.

Abstract

To understand the controllability of complex networks is a forefront problem relevant to different fields of science and engineering. Despite recent advances in network controllability theories, an outstanding issue is to understand the effect of network topology and nodal interactions on the controllability at the most fundamental level. Here we develop a universal framework based on local information only to unearth the most {\em fundamental building blocks} that determine the controllability. In particular, we introduce a network dissection process to fully unveil the origin of the role of individual nodes and links in control, giving rise to a criterion for the much needed strong structural controllability. We theoretically uncover various phase-transition phenomena associated with the role of nodes and links and strong structural controllability. Applying our theory to a large number of empirical networks demonstrates that technological networks are more strongly structurally controllable (SSC) than many social and biological networks, and real world networks are generally much more SSC than their random counterparts with intrinsic resilience and adaptability as a result of human design and natural evolution.