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Local and Consistent Centrality Measures in Networks

Author

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  • Zenou, Yves

    (Dept. of Economics, Stockholm University)

  • Dequiedt, Vianney

    (Université d’Auvergne)

Abstract

The centrality of an agent in a network has been shown to be crucial in explaining different behaviors and outcomes. In this paper, we propose an axiomatic approach to characterize a class of 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 this class of measures.

Suggested Citation

  • Zenou, Yves & Dequiedt, Vianney, 2014. "Local and Consistent Centrality Measures in Networks," Research Papers in Economics 2014:4, Stockholm University, Department of Economics.
    • Handle: RePEc:hhs:sunrpe:2014_0004
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    References listed on IDEAS

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    1. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
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    Citations

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    Cited by:

    1. Hahn, Youjin & Islam, Asadul & Patacchini, Eleonora & Zenou, Yves, 2015. "Network Structure and Education Outcomes: Evidence from a Field Experiment in Bangladesh," IZA Discussion Papers 8872, Institute of Labor Economics (IZA).
    2. Verdier, Thierry & Zenou, Yves, 2017. "The role of social networks in cultural assimilation," Journal of Urban Economics, Elsevier, vol. 97(C), pages 15-39.
    3. René van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592181, HAL.
    4. Drago, Carlo, 2015. "Exploring the Community Structure of Complex Networks," MPRA Paper 81024, University Library of Munich, Germany.
    5. Dasaratha, Krishna, 2020. "Distributions of centrality on networks," Games and Economic Behavior, Elsevier, vol. 122(C), pages 1-27.
    6. Matthew O. Jackson & Brian W. Rogers & Yves Zenou, 2017. "The Economic Consequences of Social-Network Structure," Journal of Economic Literature, American Economic Association, vol. 55(1), pages 49-95, March.
    7. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    8. Matthew Elliott & Benjamin Golub, 2019. "A Network Approach to Public Goods," Journal of Political Economy, University of Chicago Press, vol. 127(2), pages 730-776.
    9. 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.
    10. Youjin Hahn & Asadul Islam & Eleonora Patacchini & Yves Zenou, 2015. "Teams, Organization and Education Outcomes: Evidence from a field experiment in Bangladesh," Monash Economics Working Papers 35-15, Monash University, Department of Economics.
    11. 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.
    12. Drago, Carlo, 2015. "Exploring the Community Structure of Complex Networks," MPRA Paper 81024, University Library of Munich, Germany.

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    More about this item

    Keywords

    Consistency; centrality measures; networks; axiomatic approach;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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