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 \(\rho \ge 1\), 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.

中文翻译：

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抑制复杂传播在社交网络中的扩散：理论和实验结果。

我们考虑了在社交网络中抑制不良感染（例如谣言，暴民行为传播）的问题。在这种情况下，许多工作都是在1阈值模型下进行的，当一个节点只有一个邻居感染时会发生扩散。我们研究了在节点可能具有大于1的阈值的社交网络中抑制更复杂的感染的问题。目标是通过从网络中删除少量节点（称为关键节点）来最小化感染的传播。我们研究了此问题的多个版本，并证明，一般而言，除非P = NP，否则它们甚至都不能有效地近似到任何因子\（\ rho \ ge 1 \）内。。我们针对这些问题开发了高效实用的启发式方法，并在Epinions，Wikipedia和slashdot这三个著名的社交网络上对它们的性能进行了实验研究。我们的结果表明，这些启发式方法的性能明显优于其他五种已知方法。我们还针对传播可以传播到的节点数建立了一个可计算的有效上限，并在许多实际和合成网络上评估了该上限。