Optimality and Bimodality in Controlling Temporal Networks

In most complex systems, control is a central problem. Controllability of an arbitrary complex networked system means that controlling a set of driver nodes can guide the system's entire dynamics. While the properties of driver nodes set have been well characterized in static networks, very little is instead known for temporal networks, which are ubiquitous in nature. In this article, we propose to use different optimization algorithms to obtain the minimum driver nodes set in a temporal network. We then analyze the topological properties of the minimum driver nodes set, highlighting both differences and common features between temporal networks and their corresponding aggregated static networks. We show that the size of the minimum driver nodes set decreases significantly with the number of snapshots in a temporal network, which can be explained by the increase in network accessibility. Moreover, through statistical analysis of the frequency of nodes appearing in the minimum driver nodes set, we find that bimodality also appears in temporal networks. Finally, our algorithms are also applied to study the controllability of six real temporal networks.