Limiting the diffusion of information by a selective PageRank-preserving approach

The problem of limiting the diffusion of information in social networks has received substantial attention. To deal with the problem, existing works aim to prevent the diffusion of information to as many nodes as possible, by deleting a given number of edges. Thus, they assume that the diffusing information can affect all nodes and that the deletion of each edge has the same impact on the information propagation properties of the graph. In this work, we propose an approach which lifts these limiting assumptions. Our approach allows specifying the nodes to which information diffusion should be prevented and their maximum allowable activation probability, and it performs edge deletion while avoiding drastic changes to the ability of the network to propagate information. To realize our approach, we propose a measure that captures changes, caused by deletion, to the PageRank distribution of the graph. Based on the measure, we define the problem of finding an edge subset to delete as an optimization problem. We show that the problem can be modeled as a Submodular Set Cover (SSC) problem and design an approximation algorithm, based on the well-known approximation algorithm for SSC. In addition, we develop an iterative heuristic that has similar effectiveness but is significantly more efficient than our algorithm. Experiments on real and synthetic data show the effectiveness and efficiency of our methods