Highly-efficient Minimization of Network Connectivity in Large-scale Graphs

Network connectivity minimization is a fundamental problem in controlling the spread of viruses in the Internet and facilitating information propagation in online social networks. The problem aims to identify a budget number of key nodes whose removal would minimize the connectivity of a network. However, the existing solutions heavily rely on the number of edges, making it challenging to handle large and densely connected social networks. In this study, we present a fast algorithm that is independent of the number of edges. To achieve this, we first introduce a surrogate matrix that approximates the residual adjacency matrix with arbitrary small predefined error. We then devise an efficient approach for inferring k influential nodes by optimizing the eigenvalues of the surrogate matrix. Remarkably, the algorithm has a small time complexity of O(knr3), with r being a small tunable number. Our algorithm thereby maintains a linear scalability in terms of the number of nodes and is unaffected by the number of edges. Hence, it has the capability to efficiently handle large and dense social networks. At last, we evaluate its performance against state-of-the-art techniques using diverse real-world datasets. The experimental results demonstrate the superiority of our proposed method in terms of both solution quality and computational efficiency.