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Local and Consistent Centrality Measures in Networks

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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. This is possible because all the centralities study here are local in the sense that the centrality measure of an agent only depends on her set of neighbors and their centralities. Our axiomatic characterization highlights the conceptual similarities among this class of measures.

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  • Zenou, Yves & ,, 2014. "Local and Consistent Centrality Measures in Networks," CEPR Discussion Papers 10031, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:10031
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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.
    2. Mitri Kitti, 2012. "Axioms for Centrality Scoring with Principal Eigenvectors," Discussion Papers 79, Aboa Centre for Economics.
    3. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
    4. Antoni Calvó-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1239-1267.
    5. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    6. Joan Esteban & Debraj Ray, 2011. "Linking Conflict to Inequality and Polarization," American Economic Review, American Economic Association, vol. 101(4), pages 1345-1374, June.
    7. Banerjee, Abhijit & Jackson, Matthew O. & Duflo, Esther & Chandrasekhar, Arun G., 2012. "The Diffusion of Microfinance," CEPR Discussion Papers 8770, C.E.P.R. Discussion Papers.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    9. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    11. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
    12. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 441-485.
    13. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    14. Yannis M. Ioannides, 2012. "From Neighborhoods to Nations: The Economics of Social Interactions," Economics Books, Princeton University Press, edition 1, volume 1, number 9892.
    15. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    16. de Martí Beltran, Joan, 2009. "Matthew O. Jackson, Social and Economic Networks , Princeton University Press (2008)," Regional Science and Urban Economics, Elsevier, vol. 39(5), pages 644-645, September.
    17. Rajdeep Grewal & Gary L. Lilien & Girish Mallapragada, 2006. "Location, Location, Location: How Network Embeddedness Affects Project Success in Open Source Systems," Management Science, INFORMS, vol. 52(7), pages 1043-1056, July.
    18. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
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    Cited by:

    1. Verdier, Thierry & Zenou, Yves, 2017. "The role of social networks in cultural assimilation," Journal of Urban Economics, Elsevier, vol. 97(C), pages 15-39.
    2. Rene (J.R.) van den Brink & Agnieszka Rusinowska, 2017. "The Degree Measure as Utility Function over Positions in Networks," Tinbergen Institute Discussion Papers 17-065/II, Tinbergen Institute.
    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. 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.
    5. Dasaratha, Krishna, 2020. "Distributions of centrality on networks," Games and Economic Behavior, Elsevier, vol. 122(C), pages 1-27.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. Drago, Carlo, 2015. "Exploring the Community Structure of Complex Networks," MPRA Paper 81024, University Library of Munich, Germany.
    11. Drago, Carlo, 2015. "Exploring the Community Structure of Complex Networks," MPRA Paper 81024, University Library of Munich, Germany.
    12. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.

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    More about this item

    Keywords

    Axiomatic approach; Centrality measures; Consistency; Networks;
    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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