Axioms for centrality scoring with principal eigenvectors
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Techniques based on using principal eigenvector decomposition of matrices representing binary relations of sets of alternatives are commonly used in social sciences, bibliometrics, and web search engines. By representing the binary relations as a directed graph the question of ranking or scoring the alternatives can be turned into the relevant question of how to score the nodes of the graph. This paper characterizes the principal eigenvector of a matrix as a scoring function with a set of axioms. Furthermore, a method of assessing individual and group centralities simultaneously is characterized by a set of axioms. A special case of this method is the hyperlink-induced topic search for ranking websites. In general, the method can be applied to aggregation of preferences or judgments to obtain a collective assessment of alternatives.
KeywordsDirected Graph Adjacency Matrix Binary Relation Principal Eigenvalue Stochastic Matrix
I thank Hannu Salonen, Olli Lappalainen, Matti Pihlava, Jean-Jacques Herings, the associate editor, and two anonymous referees for their comments which have greatly improved this paper. I am also grateful to seminar audiences at University of Maastricht, Vrije Universiteit Amsterdam, XXXV Finnish Economic Days in Mariehamn, SING10 conference in Krakow, and 1st EUSN conference in Barcelona. Funding from the Academy of Finland is gratefully acknowledged.