IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/10031.html
   My bibliography  Save this paper

Local and Consistent Centrality Measures in Networks

Author

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP10031
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    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. 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.
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dequiedt, Vianney & Zenou, Yves, 2017. "Local and consistent centrality measures in parameterized networks," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 28-36.
    2. Zenou, Yves & Patacchini, Eleonora & Islam, Asad, 2015. "Teams, Organization and Education Outcomes: Evidence from a field experiment in Bangladesh," CEPR Discussion Papers 10631, C.E.P.R. Discussion Papers.
    3. de Marti, Joan & Zenou, Yves, 2009. "Social Networks," Working Paper Series 816, Research Institute of Industrial Economics.
    4. 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).
    5. Topa, Giorgio & Zenou, Yves, 2015. "Neighborhood and Network Effects," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 561-624, Elsevier.
    6. Ashani Amarasinghe & Roland Hodler & Paul A. Raschky & Yves Zenou, 2018. "Spatial Diffusion of Economic Shocks in Networks," CESifo Working Paper Series 7001, CESifo.
    7. de Martí, Joan & Zenou, Yves, 2015. "Network games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 221-240.
    8. Zenou, Yves & Olcina, Gonzalo & Panebianco, Fabrizio, 2017. "Conformism, Social Norms and the Dynamics of Assimilation," CEPR Discussion Papers 12166, C.E.P.R. Discussion Papers.
    9. Helsley, Robert W. & Zenou, Yves, 2014. "Social networks and interactions in cities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 426-466.
    10. Zenou, Yves, 2014. "Key Players," CEPR Discussion Papers 10277, C.E.P.R. Discussion Papers.
    11. Zenou, Yves & Lindquist, Matthew & Sauermann, Jan, 2015. "Network Effects on Worker Productivity," CEPR Discussion Papers 10928, C.E.P.R. Discussion Papers.
    12. Zenou, Yves, 2012. "Networks in Economics," CEPR Discussion Papers 9021, C.E.P.R. Discussion Papers.
    13. Verdier, Thierry & Zenou, Yves, 2017. "The role of social networks in cultural assimilation," Journal of Urban Economics, Elsevier, vol. 97(C), pages 15-39.
    14. Zenou, Yves & Patacchini, Eleonora & Liu, Xiaodong, 2013. "Peer Effects: Social Multiplier or Social Norms?," CEPR Discussion Papers 9366, C.E.P.R. Discussion Papers.
    15. Ushchev, Philip & Zenou, Yves, 2020. "Social norms in networks," Journal of Economic Theory, Elsevier, vol. 185(C).
    16. Patacchini, Eleonora & Rainone, Edoardo & Zenou, Yves, 2017. "Heterogeneous peer effects in education," Journal of Economic Behavior & Organization, Elsevier, vol. 134(C), pages 190-227.
    17. Ushchev, Philip & Zenou, Yves, 2018. "Price competition in product variety networks," Games and Economic Behavior, Elsevier, vol. 110(C), pages 226-247.
    18. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    19. Picard, Pierre M. & Zenou, Yves, 2018. "Urban spatial structure, employment and social ties," Journal of Urban Economics, Elsevier, vol. 104(C), pages 77-93.
    20. Zenou, Yves & Lindquist, Matthew, 2014. "Key Players in Co-Offending Networks," CEPR Discussion Papers 9889, C.E.P.R. Discussion Papers.

    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

    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:cpr:ceprdp:10031. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.