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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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    2. Dasaratha, Krishna, 2020. "Distributions of centrality on networks," Games and Economic Behavior, Elsevier, vol. 122(C), pages 1-27.
    3. 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.
    4. 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.
    5. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).
    6. Karol Flores-Szwagrzak & Rafael Treibich, 2020. "Teamwork and Individual Productivity," Management Science, INFORMS, vol. 66(6), pages 2523-2544, June.
    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.

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