Preventing the diffusion of information to vulnerable users while preserving PageRank

Abstract

Limiting the diffusion of information in social networks is important in viral marketing and computer security. To achieve this, existing works aim to prevent the diffusion of information to as many nodes as possible, by deleting a given number of edges. Thus, they adopt a collective approach and quantify the impact of deletion on the graph, based on the number of deleted edges. In this work, we propose a selective approach which quantifies the impact of edge deletion based on PageRank. Our approach allows specifying the nodes to which information diffusion should be prevented and their maximum allowable activation probability. Furthermore, 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. Our measure is called PageRank-Harm (PRH) and quantifies the contribution of an incoming edge $$(u_l,u)$$ to the PageRank score of the node u. Based on PRH, we define the following optimization problem: Given a subset of nodes and a threshold, find a subset of edges that has minimum PRH and whose deletion limits the activation probability of each specified node to at most the threshold. 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. Furthermore, we develop an iterative heuristic that has similar effectiveness but also enables significant computational savings. Moreover, we propose a lazy edge selection technique that is used to improve the efficiency of both our approximation algorithm and the iterative heuristic, without affecting their effectiveness. Experiments on real and synthetic data show the effectiveness and efficiency of our methods.