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

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.

16 pages, 4 figures, 1 table

References in corpus (9)

• Control Principles of Complex Networks
• Spectrum of Controlling and Observing Complex Networks
• Controllability analysis of the directed human protein interaction network identifies disease genes and drug targets
• Emergence of bimodality in controlling complex networks
• Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes
• Core percolation on complex networks
• Control of coupled oscillator networks with application to microgrid technologies
• Control of stochastic and induced switching in biophysical networks
• Control principles of metabolic networks