Blocking Simple and Complex Contagion by Edge Removal

Eliminating interactions among individuals is an important means of blocking contagion spread, e.g., closing schools during an epidemic or shutting down electronic communication channels during social unrest. We study contagion blocking in networked populations by identifying edges to remove from a network, thus blocking contagion transmission pathways. We formulate various problems to minimize contagion spread and show that some are efficiently solvable while others are formally hard. We also compare our hardness results to those from node blocking problems and show interesting differences between the two. Our main problem is not only hard, but also has no approximation guarantee, unless P=NP. Therefore, we devise a heuristic for the problem and compare its performance to state-of-the-art heuristics from the literature. We show, through results of 12 (network, heuristic) combinations on three real social networks, that our method offers considerable improvement in the ability to block contagions in weighted and unweighted networks. We also conduct a parametric study to understand the limitations of our approach.