Multi-level community-based centrality integrating local-to-global information for identifying critical components

The structural heterogeneity of complex networks across scales (local-to-global) results in critical components that disproportionately drive system functionality. Identifying and protecting critical components is of great theoretical and practical significance for ensuring the safe and efficient operation of complex systems. Recently, there has been a notable trend in applying centrality measures to identify critical components within networks. However, existing approaches rarely incorporate integrated multi-scale analysis, encompassing both local and global network properties. To fill this gap, this study proposed the Multi-level Community Structure Centrality (MCSC) method for identifying critical components. The MCSC approach employs a hierarchical community detection algorithm to capture multi-scale structural information. At each hierarchical level, the method evaluates component influence by incorporating community size, inter-community connection density, and adjacent components competition relationships. The effectiveness of the proposed method was evaluated through comprehensive testing on diverse real-world network datasets. The results demonstrate that MCSC performs well in terms of interpretability, identification accuracy, computational cost, and applicability, outperforming classical centrality measures in most networks.