A New Semi-Local Centrality with Weighted Lexicographic Extended Neighborhood (SL-WLEN) for Identifying Influential Nodes: Validation in Quality Control Networks

The identification of influential nodes in complex networks is fundamental for assessing their importance, particularly when simultaneously considering topological structure and nodal attributes. In this paper, we introduce SL-WLEN (Semi-local Centrality with Weighted and Lexicographic Extended Neighborhood), a novel centrality metric designed to identify the most influential nodes in complex networks. SL-WLEN integrates topological structure and nodal attributes by combining local components (degree and nodal values) with semi-local components (Local Relative Average Shortest Path LRASP and lexicographic ordering), thereby overcoming limitations of existing methods that treat these aspects independently. The incorporation of lexicographic ordering preserves the relative importance of nodes at each neighborhood level, ensuring that those with high values maintain their influence in the final metric without distortions from statistical aggregations. The metric was validated on a chip manufacturing quality control network comprising 1,555 nodes, where each node represents a critical process characteristic. The weighted connections between nodes reflect correlations among characteristics, enabling the evaluation of how changes propagate through the system and affect final product quality. Robustness testing demonstrates that SL-WLEN maintains high stability under various perturbations: preserving Top-1 rankings (98%) and correlations (R²>0.92) even with 50% link removal, while maintaining robustness above 80% under moderate network modifications. These findings evidence its effectiveness for complex network analysis in dynamic environments.