IDEAS home Printed from https://ideas.repec.org/p/hal/pseptp/halshs-04155088.html
   My bibliography  Save this paper

Centrality measures in networks

Author

Listed:
  • Francis Bloch

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Matthew Jackson

    (Stanford University)

  • Pietro Tebaldi

    (CUMC - Columbia University Medical Center - Columbia University [New York], NBER - National Bureau of Economic Research [New York] - NBER - The National Bureau of Economic Research)

Abstract

We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node's position in the network. This enables us to provide a taxonomy of centrality measures that distills them to varying on two dimensions: (i) which information they make use of about nodes' positions, and (ii) how that information is weighted as a function of distance from the node in question. The three sorts of information about nodes' positions that are usually used—which we refer to as "nodal statistics"—are the paths from a given node to other nodes, the walks from a given node to other nodes, and the geodesics between other nodes that include a given node. Using such statistics on nodes' positions, we also characterize the types of trees such that centrality measures all agree, and we also discuss the properties that identify some path-based centrality measures.

Suggested Citation

  • Francis Bloch & Matthew Jackson & Pietro Tebaldi, 2023. "Centrality measures in networks," PSE-Ecole d'économie de Paris (Postprint) halshs-04155088, HAL.
    • Handle: RePEc:hal:pseptp:halshs-04155088
    DOI: 10.1007/s00355-023-01456-4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    3. Dasaratha, Krishna, 2020. "Distributions of centrality on networks," Games and Economic Behavior, Elsevier, vol. 122(C), pages 1-27.
    4. Giora Slutzki & Oscar Volij, 2006. "Scoring of web pages and tournaments—axiomatizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 75-92, January.
    5. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    6. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    7. Yann Bramoullé & Garance Genicot, 2018. "Diffusion Centrality: Foundations and Extensions," Working Papers halshs-01943760, HAL.
    8. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    9. Johan Bollen & Herbert Van de Sompel & Aric Hagberg & Ryan Chute, 2009. "A Principal Component Analysis of 39 Scientific Impact Measures," PLOS ONE, Public Library of Science, vol. 4(6), pages 1-11, June.
    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. Matthew O. Jackson, 2019. "The Friendship Paradox and Systematic Biases in Perceptions and Social Norms," Journal of Political Economy, University of Chicago Press, vol. 127(2), pages 777-818.
    12. Matthew O. Jackson, 2020. "A typology of social capital and associated network measures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 311-336, March.
    13. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    Full references (including those not matched with items on IDEAS)

    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. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    2. 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.
    3. Dequiedt, Vianney & Zenou, Yves, 2017. "Local and consistent centrality measures in parameterized networks," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 28-36.
    4. Balázs Sziklai, 2018. "How to identify experts in a community?," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 155-173, March.
    5. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    6. de Martí, Joan & Zenou, Yves, 2009. "Social Networks," IZA Discussion Papers 4621, Institute of Labor Economics (IZA).
    7. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    8. Zenou, Yves & Lindquist, Matthew & Sauermann, Jan, 2015. "Network Effects on Worker Productivity," CEPR Discussion Papers 10928, C.E.P.R. Discussion Papers.
    9. Promit K. Chaudhuri & Sudipta Sarangi & Hector Tzavellas, 2023. "Games Under Network Uncertainty," Papers 2305.03124, arXiv.org, revised Jul 2023.
    10. Mitri Kitti, 2012. "Axioms for Centrality Scoring with Principal Eigenvectors," Discussion Papers 79, Aboa Centre for Economics.
    11. Dasaratha, Krishna, 2020. "Distributions of centrality on networks," Games and Economic Behavior, Elsevier, vol. 122(C), pages 1-27.
    12. Sridhar Mandyam & Usha Sridhar, 2017. "DON and Shapley Value for Allocation among Cooperating Agents in a Network: Conditions for Equivalence," Studies in Microeconomics, , vol. 5(2), pages 143-161, December.
    13. Gabrielle Demange, 2012. "On the influence of a ranking system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 431-455, July.
    14. ,, 2014. "A ranking method based on handicaps," Theoretical Economics, Econometric Society, vol. 9(3), September.
    15. Hannu Salonen, 2014. "Aggregating and Updating Information," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(2), pages 55-67, October.
    16. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    17. Harkins, Andrew, 2020. "Network Comparative Statics," The Warwick Economics Research Paper Series (TWERPS) 1306, University of Warwick, Department of Economics.
    18. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).
    19. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    20. Goyal, S., 2018. "Heterogeneity and Networks," Cambridge Working Papers in Economics 1812, Faculty of Economics, University of Cambridge.

    More about this item

    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:hal:pseptp:halshs-04155088. 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: Caroline Bauer (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.