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Local and consistent centrality measures in parameterized networks

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  • Vianney Dequiedt

    (CERDI - Centre d'Études et de Recherches sur le Développement International - UCA [2017-2020] - Université Clermont Auvergne [2017-2020] - CNRS - Centre National de la Recherche Scientifique)

  • Yves Zenou

    (IFN - Institutet för Näringslivsforskning - Department of Economics - Monash University)

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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  • Vianney Dequiedt & Yves Zenou, 2017. "Local and consistent centrality measures in parameterized networks," Post-Print halshs-01528908, HAL.
    • Handle: RePEc:hal:journl:halshs-01528908
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01528908
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    3. Karol Flores-Szwagrzak & Rafael Treibich, 2020. "Teamwork and Individual Productivity," Management Science, INFORMS, vol. 66(6), pages 2523-2544, June.
    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. 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.
    6. Dasaratha, Krishna, 2020. "Distributions of centrality on networks," Games and Economic Behavior, Elsevier, vol. 122(C), pages 1-27.
    7. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).

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