Analysis of Controllability for Temporal Networks

Abstract

Physical systems modeled by networks are fully dynamic in the sense that the process of adding edges and vertices never ends, and no edge or vertex is necessarily eternal. Temporal networks enable to explicitly study systems with a changing topology by capturing explicitly the temporal changes. The controllability of temporal networks is the study of driving the state of a temporal network to a target state at deadline tf within △t = tf - t0 steps by stimulating key nodes called driver nodes. In this research, the author aims to understand and analyze temporal networks from the controllability perspective at the global and nodal scales. To analyze the controllability at global scale, the author provides an efficient heuristic algorithm to build driver node sets capable of fully controlling temporal networks. At the nodal scale, the author presents the concept of Complete Controllable Domain (CCD) to investigate the characteristics of Maximum Controllable Subspaces (MCSs) of a driver node. The author shows that a driver node can have an exponential number of MCSs and introduces a branch and bound algorithm to approximate the CCD of a driver node. The proposed algorithms are evaluated on real-world temporal networks induced from ant interactions in six colonies and in a set of e-mail communications of a manufacturing company. At the global scale, the author provides ways to determine the control regime in which a network operates. Through empirical analysis, the author shows that ant interaction networks operate under a distributed control regime whereas the e-mails network operates in a centralized regime. At the nodal scale, the analysis indicated that on average the number of nodes that a driver node always controls is equal to the number of driver nodes that always control a node.