A new measure to assess the centrality of vertices in an undirected and connected graph is proposed. The proposed measure, L1 centrality, can adequately handle graphs with weights assigned to vertices and edges. The 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, local L1 centrality, multiscale edge representation, and heterogeneity plot and index. 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 the paper, 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.

翻译：提出了一种评估无向连通图中顶点中心性的新测度。该测度（L1中心性）能够妥善处理顶点和边赋权图。研究提供了基于L1中心性的图形化与多尺度分析工具，具体包括目标图、L1中心性邻域、局部L1中心性、多尺度边表示以及异质性图与指数。最重要的贡献在于，本工作与多元数据的数据深度概念紧密关联，这使得所提测度具有广泛的实践应用前景。全文通过漫威电影宇宙关系网和韩国第21届国会法案共同发起网络两个典型案例，对分析工具进行了系统展示。