On a Notion of Graph Centrality Based on L1 Data Depth

A new measure, L1 centrality, is proposed to assess the centrality of vertices in an undirected and connected graph. The proposed measure can adequately handle graphs with weights assigned to vertices and edges. This study provides tools for graphical and multiscale analysis based on the L1 centrality. Specifically, the suggested analysis tools include the target plot, L1 centrality-based neighborhood, and local L1 centrality. Most importantly, our work is closely associated with the concept of data depth for multivariate data, which allows for a wide range of practical applications of the proposed measure. Throughout this article, we demonstrate our tools with two interesting examples: the Marvel Cinematic Universe movie network and the bill cosponsorship network of the 21st National Assembly of South Korea. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.