IDEAS home Printed from https://ideas.repec.org/p/hhs/sunrpe/2014_0004.html
   My bibliography  Save this paper

Local and Consistent Centrality Measures in Networks

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www2.ne.su.se/paper/wp14_04.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    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. N. Lesca, 2011. "Introduction," Post-Print halshs-00640604, HAL.
    8. Banerjee, Abhijit & Chandrasekhar, Arun G & Duflo, Esther & Jackson, Matthew O., 2012. "The Diffusion of Microfinance," CEPR Discussion Papers 8770, C.E.P.R. Discussion Papers.
    9. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    10. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, Oxford University Press, vol. 122(2), pages 441-485.
    11. 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.
    12. Yannis M. Ioannides, 2012. "From Neighborhoods to Nations: The Economics of Social Interactions," Economics Books, Princeton University Press, edition 1, number 9892.
    13. 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.
    14. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    15. 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.
    16. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Krishna Dasaratha, 2017. "Distributions of Centrality on Networks," Papers 1709.10402, arXiv.org, revised Jan 2018.
    3. 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 for the Study of Labor (IZA).
    4. René van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Documents de travail du Centre d'Economie de la Sorbonne 17035, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. 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.
    6. 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.
    7. Drago, Carlo, 2015. "Exploring the Community Structure of Complex Networks," MPRA Paper 81024, University Library of Munich, Germany.
    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. Verdier, Thierry & Zenou, Yves, 2017. "The role of social networks in cultural assimilation," Journal of Urban Economics, Elsevier, vol. 97(C), pages 15-39.
    10. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    11. 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.
    12. Elliott, M. & Golub, B., 2018. "A Network Approach to Public Goods," Cambridge Working Papers in Economics 1813, Faculty of Economics, University of Cambridge.

    More about this item

    Keywords

    Consistency; centrality measures; networks; axiomatic approach;

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:sunrpe:2014_0004. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sten Nyberg). General contact details of provider: http://edirc.repec.org/data/neisuse.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.