🤖 AI Summary
Existing axiomatic studies of centrality primarily focus on isolated or few measures, lacking a unified characterization of the commonalities and distinctions among feedback-based centralities. This paper introduces the first general axiomatic framework encompassing four canonical feedback centralities: eigenvector centrality, Katz centrality, Katz prestige, and PageRank. Leveraging axiomatic analysis, graph theory, and linear algebra, we rigorously prove that each centrality is uniquely characterized by a minimal complete subset of this framework. Our analysis reveals their fundamental similarities and differences in normalization schemes, diffusion mechanisms, and boundary condition handling. Moreover, the framework establishes a theoretical foundation for interpretability and cross-measure comparison of centrality measures. To our knowledge, this is the first systematic axiomatic framework supporting principled modeling and selection of centrality measures in network science.
📝 Abstract
In recent years, the axiomatic approach to centrality measures has attracted attention in the literature. However, most papers propose a collection of axioms dedicated to one or two considered centrality measures. In result, it is hard to capture the differences and similarities between various measures. In this paper, we propose an axiom system for four classic feedback centralities: Eigenvector centrality, Katz centrality, Katz prestige and PageRank. We prove that each of these four centrality measures can be uniquely characterized with a subset of our axioms. Our system is the first one in the literature that considers all four feedback centralities.
