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Axioms for centrality scoring with principal eigenvectors

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  • Mitri Kitti

    (University of Turku)

Abstract

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.

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  • Mitri Kitti, 2016. "Axioms for centrality scoring with principal eigenvectors," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 639-653, March.
    • Handle: RePEc:spr:sochwe:v:46:y:2016:i:3:d:10.1007_s00355-015-0931-2
    DOI: 10.1007/s00355-015-0931-2
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    Cited by:

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    3. L'aszl'o Csat'o & Csaba T'oth, 2018. "University rankings from the revealed preferences of the applicants," Papers 1810.04087, arXiv.org, revised Feb 2020.
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    6. Rene (J.R.) van den Brink & Agnieszka Rusinowska, 2017. "The Degree Measure as Utility Function over Positions in Networks," Tinbergen Institute Discussion Papers 17-065/II, Tinbergen Institute.
    7. Daniela Bubboloni & Michele Gori, 2018. "The flow network method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 621-656, December.
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    10. Csató, László & Tóth, Csaba, 2020. "University rankings from the revealed preferences of the applicants," European Journal of Operational Research, Elsevier, vol. 286(1), pages 309-320.

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