Twenty Years of Network Science: From Structure to Control

Systems as diverse as the cell, the brain, the World Wide Web, or the social systems are described by highly interconnected networks with complex topology, whose structure determines their function and utility. Twenty years a research has shown that these networks are the result of self-organizing processes governed by simple but generic laws, that can be best understood using tools rooted in statistical physics. These studies have also offered evidence of a deep universality, finding that many real networks share multiple common architectural features, from the scale-free property, discovered 20 year ago today, to communities and correlations. I will discuss the order characterizing real networks and its implication, with focus on network control. Indeed, most complex systems have purpose, striving to accomplish some function, from the cell’s ability to reproduce to the brain’s ability to control our motions. For this, the underlying networks must be wired to be able to constantly control the system’s internal processes, in response to external inputs and perturbations. I will show how to adapt the tools of control theory to unveil the control principles of complex self-organized systems. Finally, I will discuss a recently developed analytical framework to study the controllability of an arbitrary complex network, and offer experimental evidence for its direct applicability to neural networks in the brain.