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Axioms for Centrality Scoring with Principal Eigenvectors

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  • Mitri Kitti

    (Department of Economics, Turku School of Economics, 20014 University of Turku, Finland)

Abstract

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.

Suggested Citation

  • Mitri Kitti, 2012. "Axioms for Centrality Scoring with Principal Eigenvectors," Discussion Papers 79, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp79
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    References listed on IDEAS

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    Cited by:

    1. Hannu Salonen, 2016. "Equilibria and centrality in link formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1133-1151, November.
    2. Zenou, Yves & Dequiedt, Vianney, 2014. "Local and Consistent Centrality Measures in Networks," Research Papers in Economics 2014:4, Stockholm University, Department of Economics.
    3. László Csató, 2017. "Measuring centrality by a generalization of degree," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 771-790, December.
    4. Hannu Salonen, 2015. "Bonacich Measures as Equilibria in Network Models," Discussion Papers 100, Aboa Centre for Economics.
    5. Abigail Paradise & Asaf Shabtai & Rami Puzis, 2019. "Detecting Organization-Targeted Socialbots by Monitoring Social Network Profiles," Networks and Spatial Economics, Springer, vol. 19(3), pages 731-761, September.

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    More about this item

    Keywords

    principal eigenvector; graph; centrality; scoring; axiom;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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