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When to target hubs? Strategic Diffusion in Complex Networks

Aamena Alshamsi, Flavio L. Pinheiro, Cesar A. Hidalgo

posted on 02 May 2017

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What is the most effective way to spread a behavior on a network? The recent literature on network diffusion has focused mostly on models of simple contagion---where contagion can result from contact with a single "infected" individual---and complex contagion---where contagion requires contact with multiple "infected" sources. While in the case of simple contagion, strategies focused on central nodes are known to be effective, the strategies that are most effective in the case of complex contagion are relatively unknown. Here, we study the strategies that optimize the diffusion of a behavior on a network in the case of complex contagion by comparing algorithms that choose which nodes to target at each step. We find that, contrary to the case of simple contagion, where targeting central nodes is an effective strategy, in the case of complex contagion minimizing the total diffusion time requires the use of dynamic strategies targeting less connected nodes in the beginning and hubs at a critical intermediate time. That is, the strategic question in the case of complex contagion is not who to target, but when to target hubs. We solve the model analytically for simple network structures and also use numerical simulations to show that these dynamic strategies outperform simpler strategies that could be hypothesized to be effective, like always choosing the node with the highest probability of infection. These findings shed light on the dynamic strategies that optimize network diffusion in the case of complex contagion.