SL-WLEN, a Novel Semi-Local Centrality Metric with Weighted Lexicographic Extended Neighborhood for Identifying Influential Nodes in Networks with Weighted Edges and Nodal Attributes

The identification of influential nodes in complex networks modeling manufacturing environments is a critical aspect, especially when considering both structure and nodal attributes. This becomes particularly relevant given that conventional weighted centrality measures typically only consider edge weights while ignoring node heterogeneity. We present SL-WLEN (Semi-Local centrality with Weighted Lexicographic Extended Neighborhood), a novel centrality metric designed to overcome these limitations. Based on LRASP (Local Relative Average Shortest Path) and lexicographic ordering, SL-WLEN integrates topological structure and nodal attributes by combining local components (degree and nodal values). 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. This method is applied and its robustness evaluated in a quality control network for chip manufacturing, comprising 1555 nodes representing critical process characteristics, with weighted connections indicating their degree of correlation. Finally, the metric was evaluated against other established methods using the SIR propagation model and Kendall’s τ coefficient, demonstrating that SL-WLEN maintains consistent values across all analyzed test networks.