On a Notion of Graph Centrality Based on L1 Data Depth

TL;DR

This paper introduces L1 centrality, a novel graph centrality measure based on data depth, enabling multiscale analysis of weighted graphs with practical applications demonstrated on movie and legislative networks.

Contribution

The paper proposes L1 centrality, integrating data depth concepts into graph analysis, along with new tools for multiscale and heterogeneity analysis of weighted graphs.

Findings

L1 centrality effectively captures vertex importance in weighted graphs.

New visualization tools facilitate multiscale analysis of complex networks.

Applications demonstrate the measure's usefulness in real-world networks.

Abstract

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.