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Local and consistent centrality measures in parameterized networks

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  • Dequiedt, Vianney
  • Zenou, Yves

Abstract

We propose an axiomatic approach to characterize centrality measures for which the centrality of an agent is recursively related to the centralities of the agents she is connected to. This includes the Katz–Bonacich and the eigenvector centrality. The core of our argument hinges on the power of the consistency axiom, which relates the properties of the measure for a given network to its properties for a reduced problem. In our case, the reduced problem only keeps track of local and parsimonious information. Our axiomatic characterization highlights the conceptual similarities among those measures.

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  • Dequiedt, Vianney & Zenou, Yves, 2017. "Local and consistent centrality measures in parameterized networks," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 28-36.
    • Handle: RePEc:eee:matsoc:v:88:y:2017:i:c:p:28-36
    DOI: 10.1016/j.mathsocsci.2017.04.002
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    Cited by:

    1. René Van Den Brink & Agnieszka Rusinowska, 2023. "Degree Centrality, von Neumann-Morgenstern Expected Utility and Externalities in Networks," Documents de travail du Centre d'Economie de la Sorbonne 23012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    3. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).
    4. Karol Flores-Szwagrzak & Rafael Treibich, 2020. "Teamwork and Individual Productivity," Management Science, INFORMS, vol. 66(6), pages 2523-2544, June.
    5. Francis Bloch & Matthew O. Jackson & Pietro Tebaldi, 2023. "Centrality measures in networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 413-453, August.
    6. Dasaratha, Krishna, 2020. "Distributions of centrality on networks," Games and Economic Behavior, Elsevier, vol. 122(C), pages 1-27.
    7. Anindya S. Chakrabarti & Sanjay Moorjani, 2021. "Strategic Connections in a Hierarchical Society: Wedge Between Observed and Fundamental Valuations," Dynamic Games and Applications, Springer, vol. 11(3), pages 433-462, September.
    8. René Van Den Brink & Agnieszka Rusinowska, 2023. "Degree Centrality, von Neumann-Morgenstern Expected Utility and Externalities in Networks," Documents de travail du Centre d'Economie de la Sorbonne 23012r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jun 2024.

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