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The concept of k-core, which indicates the largest induced subgraph whereeach node has k or more neighbors, plays a significant role in measuring thecohesiveness and the engagement of a network, and it is exploited in diverseapplications, e.g., network analysis, anomaly detection, community detection,etc. Recent works have demonstrated the vulnerability of k-core under maliciousperturbations which focuses on removing the minimal number of edges to make awhole k-core structure collapse. However, to the best of our knowledge, thereis no existing research concentrating on how many edges should be removed atleast to make an arbitrary node in k-core collapse. Therefore, in this paper,we make the first attempt to study the Targeted k-node Collapse Problem (TNCP)with four novel contributions. Firstly, we offer the general definition of TNCPproblem with the proof of its NP-hardness. Secondly, in order to address theTNCP problem, we propose a heuristic algorithm named TNC and its improvedversion named ATNC for implementations on large-scale networks. After that, theexperiments on 16 real-world networks across various domains verify thesuperiority of our proposed algorithms over 4 baseline methods along withdetailed comparisons and analyses. Finally, the significance of TNCP problemfor precisely evaluating the resilience of k-core structures in networks isvalidated.

Targeted k-node Collapse Problem: Towards Understanding the Robustness of Local k-core Structure