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Local and Consistent Centrality Measures in Networks

  • Zenou, Yves

    ()

    (Dept. of Economics, Stockholm University)

  • Dequiedt, Vianney

    ()

    (Université d’Auvergne)

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.

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Paper provided by Stockholm University, Department of Economics in its series Research Papers in Economics with number 2014:4.

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Length: 25 pages
Date of creation: 21 May 2014
Date of revision:
Handle: RePEc:hhs:sunrpe:2014_0004
Contact details of provider: Postal: Department of Economics, Stockholm, S-106 91 Stockholm, Sweden
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Fax: +46 8 16 14 25
Web page: http://www.ne.su.se/
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  1. Yannis M. Ioannides, 2012. "From Neighborhoods to Nations: The Economics of Social Interactions," Economics Books, Princeton University Press, edition 1, volume 1, number 9892.
  2. Ballester, Coralio & Calvó-Armengol, Antoni & Zenou, Yves, 2005. "Who’s Who in Networks. Wanted: The Key Player," CEPR Discussion Papers 5329, C.E.P.R. Discussion Papers.
  3. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-51, July.
  4. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
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  6. 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.
  7. Joan Esteban & Debraj Ray, 2009. "Linking Conflict to Inequality and Polarization," UFAE and IAE Working Papers 766.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 25 Mar 2010.
  8. Peleg, B. & Tijs, S.H., 1996. "The consistency principle for games in strategic form," Other publications TiSEM fc27db2d-b84c-44ba-95a1-0, Tilburg University, School of Economics and Management.
  9. Fryer, Roland & Echenique, Federico, 2007. "A Measure of Segregation Based on Social Interactions," Scholarly Articles 2958220, Harvard University Department of Economics.
  10. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer, vol. 18(1), pages 39-43, March.
  11. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
  12. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  13. 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.
  14. Mitri Kitti, 2012. "Axioms for Centrality Scoring with Principal Eigenvectors," Discussion Papers 79, Aboa Centre for Economics.
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