IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v43y2018i4p1085-1118.html
   My bibliography  Save this article

How to Calculate the Barycenter of a Weighted Graph

Author

Listed:
  • Sébastien Gadat

    (Toulouse School of Economics, Université Toulouse 1 Capitole, 31042 Toulouse, France)

  • Ioana Gavra

    (Institut de Mathématiques de Toulouse, Université Toulouse 3 Paul Sabatier, 31400 Toulouse, France)

  • Laurent Risser

    (Institut de Mathématiques de Toulouse, CNRS, 31400 Toulouse, France)

Abstract

Discrete structures like graphs make it possible to naturally and flexibly model complex phenomena. Since graphs that represent various types of information are increasingly available today, their analysis has become a popular subject of research. Yet, even an algorithm for locating the average position in graphs is lacking although this knowledge would be of primary interest for statistical analysis or representation problems. In this work, we develop a stochastic algorithm for finding the Fréchet mean of weighted undirected metric graphs. This method relies on a noisy simulated annealing algorithm dealt with using homogenization. We then illustrate our algorithm with three examples (subgraphs of a social network, subgraph of a collaboration and citation network, and a transport network).

Suggested Citation

  • Sébastien Gadat & Ioana Gavra & Laurent Risser, 2018. "How to Calculate the Barycenter of a Weighted Graph," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1085-1118, November.
    • Handle: RePEc:inm:ormoor:v:43:y:2018:i:4:p:1085-1118
    DOI: 10.1287/moor.2017.0896
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/moor.2017.0896
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2017.0896?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hakimi, S. Louis, 1983. "On locating new facilities in a competitive environment," European Journal of Operational Research, Elsevier, vol. 12(1), pages 29-35, January.
    2. Olga Klopp & Alexandre Tsybakov & Nicolas Verzelen, 2016. "Oracle inequalities for network models and sparse graphon estimation," Working Papers 2016-13, Center for Research in Economics and Statistics.
    3. Daron Acemoğlu & Giacomo Como & Fabio Fagnani & Asuman Ozdaglar, 2013. "Opinion Fluctuations and Disagreement in Social Networks," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 1-27, February.
    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. Crespo, Marelys & Gadat, Sébastien & Gendre, Xavier, 2023. "Stochastic Langevin Monte Carlo for (weakly) log-concave posterior distributions," TSE Working Papers 23-1398, Toulouse School of Economics (TSE).
    2. Steffen Borgwardt, 2022. "An LP-based, strongly-polynomial 2-approximation algorithm for sparse Wasserstein barycenters," Operational Research, Springer, vol. 22(2), pages 1511-1551, April.

    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. Freire, Alexandre S. & Moreno, Eduardo & Yushimito, Wilfredo F., 2016. "A branch-and-bound algorithm for the maximum capture problem with random utilities," European Journal of Operational Research, Elsevier, vol. 252(1), pages 204-212.
    2. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    3. Xiang Li & Tianyu Zhang & Liang Wang & Hongguang Ma & Xiande Zhao, 2022. "A minimax regret model for the leader–follower facility location problem," Annals of Operations Research, Springer, vol. 309(2), pages 861-882, February.
    4. U. Seppaelae, 1997. "An Evolutionary Model for Spatial Location of Economic Facilities," Working Papers ir97003, International Institute for Applied Systems Analysis.
    5. Thomas Byrne & Sándor P. Fekete & Jörg Kalcsics & Linda Kleist, 2023. "Competitive location problems: balanced facility location and the One-Round Manhattan Voronoi Game," Annals of Operations Research, Springer, vol. 321(1), pages 79-101, February.
    6. Prummer, Anja & Siedlarek, Jan-Peter, 2017. "Community leaders and the preservation of cultural traits," Journal of Economic Theory, Elsevier, vol. 168(C), pages 143-176.
    7. Mohamed Mostagir & James Siderius, 2023. "Social Inequality and the Spread of Misinformation," Management Science, INFORMS, vol. 69(2), pages 968-995, February.
    8. R. Suárez-Vega & D. Santos-Peñate & P. Dorta-González, 2004. "Discretization and resolution of the (r|X p )-medianoid problem involving quality criteria," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 111-133, June.
    9. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska, 2023. "On the Design of Public Debate in Social Networks," Operations Research, INFORMS, vol. 71(2), pages 626-648, March.
    10. Gentile, José & Alves Pessoa, Artur & Poss, Michael & Costa Roboredo, Marcos, 2018. "Integer programming formulations for three sequential discrete competitive location problems with foresight," European Journal of Operational Research, Elsevier, vol. 265(3), pages 872-881.
    11. Michler, Jeffrey D. & Gramig, Benjamin M., 2012. "Differentiation in a Two-Dimensional Market with Endogenous Sequential Entry," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 124845, Agricultural and Applied Economics Association.
    12. Marina Azzimonti-Renzo & Alessandra Fogli & Fabrizio Perri & Mark Ponder, 2020. "Pandemic Control in ECON-EPI Networks," Staff Report 609, Federal Reserve Bank of Minneapolis.
    13. Prummer, Anja & Siedlarek, Jan-Peter, 2014. "Institutions And The Preservation Of Cultural Traits," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 470, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    14. Rafael Suárez-Vega & Dolores Santos-Peñate & Pablo Dorta-González, 2014. "Location and quality selection for new facilities on a network market," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(2), pages 537-560, March.
    15. Jiangbo Zhang & Yiyi Zhao, 2023. "Dynamics Analysis for the Random Homogeneous Biased Assimilation Model," Mathematics, MDPI, vol. 11(7), pages 1-17, March.
    16. Drezner, Tammy & Drezner, Zvi & Salhi, Said, 2002. "Solving the multiple competitive facilities location problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 138-151, October.
    17. Merlone, U. & Radi, D., 2014. "Reaching consensus on rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 260-271.
    18. Godinho, Pedro & Dias, Joana, 2013. "Two-player simultaneous location game: Preferential rights and overbidding," European Journal of Operational Research, Elsevier, vol. 229(3), pages 663-672.
    19. Antonio Jiménez-Martínez, 2015. "A model of belief influence in large social networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 21-59, May.
    20. He, Zhou & Han, Guanghua & Cheng, T.C.E. & Fan, Bo & Dong, Jichang, 2019. "Evolutionary food quality and location strategies for restaurants in competitive online-to-offline food ordering and delivery markets: An agent-based approach," International Journal of Production Economics, Elsevier, vol. 215(C), pages 61-72.

    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:inm:ormoor:v:43:y:2018:i:4:p:1085-1118. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.