Critical Nodes Detection: Node Merging Approach

Hongbo Qiu, Renjie Sun, Chen Chen, Xiaoyang Wang, Ying Zhang

Abstract: Various cohesive models are widely employed for the analysis of social networks to identify critical users or key relationships, with the k-core being a particularly popular approach. Existing works, such as the anchor k-core problem, aim to maximize k-core by anchoring nodes (the degree of anchor nodes are set as infinity). However, we find that node merging can also enlarge the k-core size. Different from anchoring nodes, nodes merging can cause both degree increase and decrease which brings more challenges. In this paper, we study the <u>c</u>ore <u>m</u>aximization by <u>n</u>ode <u>m</u>erging problem (CMNM) and prove its hardness. A greedy framework is first presented due to its hardness. To scale for large networks, we categorize potentially influential nodes and provide a detailed analysis of all node merging pairs. Then, based on these analyses, a fast and effective algorithm is developed. Finally, we conduct comprehensive experiments on real-world networks to evaluate the effectiveness and efficiency of the proposed method.