Controlling Complex Networks via Influence

Human behavior is profoundly affected by individuals and the social network that links them together. We base our study on the important model of influence network largely due to DeGroot. In this model, the social structure of a society is described by a weighted and possibly directed network. Each node in the network takes an initial position about a common question of interest. At each date, nodes communicate with each other in the social network and update their positions because of the influences from neighbors. This paper presents a framework to analyze the controllability of social complex networks via influence. We show how the opinion, or attitude about some common questions can be controlled by a subset of committed nodes who consistently proselytize the opposing opinion and are immune to influence. Some controllable criteria are established to guarantee that a network can be fully or partially controllable. Besides, the methods to control an influence network are proposed. Because structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks in the physical and life sciences, the relationship between influence controllability and structural controllability of networks is also presented.