Title: Disrupting Diffusion: Critical Nodes in Network
Abstract: We formulate and study the problem of identifying nodes whose absence can maximally disrupt network-diffusion under independent cascade model. We refer to such nodes as critical nodes. We present the notion of impact and characterize critical nodes based on this notion. Informally, impact of a set of nodes quantifies the necessity of the nodes in the diffusion process. We prove that the impact is monotonic.
Interestingly, unlike similar formulation of critical edges in the context of Linear Threshold diffusion model, impact is neither submodular nor supermodular. Hence, we develop heuristics that rely on greedy strategy and modular or submodular approximations of impact function. We empirically evaluate our heuristics by comparing the level of disruption achieved by identifying and removing critical nodes as opposed to that achieved by removing the most influential nodes.