A Fast Algorithm for Moderating Critical Nodes via Edge Removal
Changan Liu, Xiaotian Zhou, Ahad N. Zehmakan, Zhongzhi Zhang
Abstract
Critical nodes in networks are extremely vulnerable to malicious attacks to trigger negative cascading events such as the spread of misinformation and diseases. Therefore, effective moderation of critical nodes is very vital for mitigating the potential damages caused by such malicious diffusions. The current moderation methods are computationally expensive. Furthermore, they disregard the fundamental metric of information centrality, which measures the dissemination power of nodes. We investigate the problem of removing <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> edges from a network to minimize the information centrality of a target node <inline-formula><tex-math notation="LaTeX">$v$</tex-math></inline-formula> while preserving the network's connectivity. We prove that this problem is computationally challenging: it is NP-complete and its objective function is not supermodular. However, we propose three approximation greedy algorithms using novel techniques such as random walk-based Schur complement approximation and fast sum estimation. One of our algorithms runs in nearly linear time in the number of edges. To complement our theoretical analysis, we conduct a comprehensive set of experiments on synthetic and real networks with over one million nodes. Across various settings, the experimental results illustrate the effectiveness and efficiency of our proposed algorithms.