Axioms for Centrality Scoring with Principal Eigenvectors

Techniques based on using principal eigenvectors of matrices representing binary relations of sets of alternatives are commonly used in social sciences, bibliometrics, and web search engines. In most applications the binary relations can be represented by a directed graph and the question of ranking or scoring the alternatives can be turned into the question of assessing the centrality of nodes of the graph. This paper characterizes the principal eigenvector as a scoring function with a set of axioms. A zero-sum scoring function based on the difference of principal right and left eigenvectors is introduced and axiomatized. Furthermore, a method of assessing individual and group centralities simultaneously is characterized by a set of axioms. The specific case of this method is the Hyperlink-Induced Topic Search (HITS) used in ranking web sites.