Disabling External Influence in Social Networks via Edge Recommendation

Abstract: Existing socio-psychological studies suggest that users of a social network form their opinions relying on the opinions of their neighbors. According to DeGroot opinion formation model, one value of particular importance is the asymptotic consensus value---the sum of user opinions weighted by the users' eigenvector centralities. This value plays the role of an attractor for the opinions in the network and is a lucrative target for external influence. However, since any potentially malicious control of the opinion distribution in a social network is clearly undesirable, it is important to design methods to prevent the external attempts to strategically change the asymptotic consensus value. In this work, we assume that the adversary wants to maximize the asymptotic consensus value by altering the opinions of some users in a network; we, then, state DIVER---an NP-hard problem of disabling such external influence attempts by strategically adding a limited number of edges to the network. Relying on the theory of Markov chains, we provide perturbation analysis that shows how eigenvector centrality and, hence, DIVER's objective function change in response to an edge's addition to the network. The latter leads to the design of a pseudo-linear-time heuristic for DIVER, whose computation relies on efficient estimation of mean first passage times in a Markov chain. We confirm our theoretical findings in experiments.