Inference of Hidden Social Power Through Opinion Formation in Complex Networks

Social networks analysis and mining gets ever-increasing importance in various disciplines. In this context finding the most influential nodes with the highest social power is important in many applications including spreading of innovation, opinion formation, immunization, information propagation and recommendation. In this manuscript, we propose a mathematical framework in order to effectively estimate the social power (influence) of nodes from time series of their interactions. We assume that there is a connection network on which the nodes interact and exchange their opinions. The time series of the opinion values (with hidden social power values) are taken as input to the proposed formalism and an optimization approach results the estimated for the social power values. We propose an estimation framework based on Maximum-a-Posteriori method that can be converted to a convex optimization problem using Jensen inequality. We apply the proposed method on a number of model networks and show that it correctly estimates the true values of the social power. The proposed method is not sensitive to the specific form of social power used to produce the time series of the opinion values. We also consider an application of finding influential nodes in opinion formation through informed agents. In this application, the problem is to find a number of influential nodes to which the informed agents should be connected to maximize their influence. Our numerical simulations show that the proposed method outperforms classical heuristic methods including connecting the informed agents to nodes with the highest degree, betweenness, closeness, PageRank centralities or based on a state-of-the-art opinion-based model.