Controllability limit of edge dynamics in complex networks.

Edge dynamics is relevant to various real-world systems with complex network topological features. An edge dynamical system is controllable if it can be driven from any initial state to any desired state in finite time with appropriate control inputs. Here a framework is proposed to study the impact of correlation between in- and out-degrees on controlling the edge dynamics in complex networks. We use the maximum matching and direct acquisition methods to determine the controllability limit, i.e., the limit of acceptable change of the edge controllability by adjusting the degree correlation only. Applying the framework to plenty complex networks, we find that the controllability limits are ubiquitous in model and real networks. Arbitrary edge controllability in between the limits can be achieved by properly adjusting the degree correlation. Moreover, a nonsmooth phenomenon occurs in the upper limits, and exponential and power-law scaling behaviors are widespread in the approach or separation speed between the upper and lower limits.