Control efficacy of complex networks.
Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver nodes. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks.
School of Systems Science, Beijing Normal University, Beijing, 100875, P. R. China.
Xin-Dong
XD
Gao
School of Systems Science, Beijing Normal University, Beijing, 100875, P. R. China.|Business School, University of Shanghai for Science and Technology, Shanghai 200093, China.
Wen-Xu
WX
Wang
School of Electrical, Compute and Energy Engineering, Arizona State University, Tempe, Arizona, 85287 USA.|Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.
Ying-Cheng
YC
Lai