Adaptive multi-scale hierarchical method for complex network key nodes identification

Traditional centrality measures normally rely on a single topological scale, which limits their ability to comprehensively characterize the roles of nodes across local, semi-local, and global network structures. Moreover, their generalization capability across different network types is often weak, leading to low accuracy in identifying key nodes. To solve these limitations, this paper has proposed an adaptive multi-scale hierarchical method for key nodes identification in complex networks, called AdaMH. First, a hierarchical structural influence framework is constructed by integrating local, semi-local, and global topological scales. Second, an adaptive entropy weight allocation strategy based on information entropy is employed to achieve robust fusion of multi-scale structural features. Finally, extensive comparative analysis experiments are conducted on nine real-world datasets against five well-known baseline methods. Experimental results under the SIR spreading model prove that the top-10 nodes identified by AdaMH increase the final infection range by 1% to 156% compared with baseline methods. These results indicate that AdaMH effectively captures synergistic relations among multi-scale structural features, thereby providing an efficient identification of key nodes. In addition, the proposed method can also be applied in the field of fraudulent node mining.