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

Disabling External Influence in Social Networks via Edge Recommendation