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We consider the problem of inhibiting undesirable contagions (e.g. rumors, spread of mob behavior) in social networks. Much of the work in this context has been carried out under the 1-threshold model, where diffusion occurs when a node has just one neighbor with the contagion. We study the problem of inhibiting more complex contagions in social networks where nodes may have thresholds larger than 1. The goal is to minimize the propagation of the contagion by removing a small number of nodes (called critical nodes ) from the network. We study several versions of this problem and prove that, in general, they cannot even be efficiently approximated to within any factor ρ ≥ 1, unless P = NP . We develop efficient and practical heuristics for these problems and carry out an experimental study of their performance on three well known social networks, namely epinions, wikipedia and slashdot. Our results show that these heuristics perform significantly better than five other known methods. We also establish an efficiently computable upper bound on the number of nodes to which a contagion can spread and evaluate this bound on many real and synthetic networks.

Inhibiting diffusion of complex contagions in social networks: theoretical and experimental results