IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0339060.html

Detection of an arbitrary number of communities in a block spin Ising model

Author

Listed:
  • Miguel Ballesteros
  • Ramsès H Mena
  • Josè Luis Pèrez
  • Gabor Toth

Abstract

We study the problem of community detection in a general version of the block spin Ising model featuring M groups, a model inspired by the Curie-Weiss model of ferromagnetism in statistical mechanics. We solve the general problem of identifying any number of groups with any possible coupling constants. Up to now, the problem was only solved for the specific situation with two groups of identical size and identical interactions, see [1, 2]. Our results can be applied to the most realistic situations, in which there are many groups of different sizes and different interactions. In addition, we give an explicit algorithm that permits the reconstruction of the structure of the model from a sample of observations based on the comparison of empirical correlations of the spin variables, thus unveiling easy applications of the model to real-world voting data and communities in biology.

Suggested Citation

  • Miguel Ballesteros & Ramsès H Mena & Josè Luis Pèrez & Gabor Toth, 2026. "Detection of an arbitrary number of communities in a block spin Ising model," PLOS ONE, Public Library of Science, vol. 21(3), pages 1-33, March.
    • Handle: RePEc:plo:pone00:0339060
    DOI: 10.1371/journal.pone.0339060
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0339060
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0339060&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0339060?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
    ---><---

    References listed on IDEAS

    as
    1. Pierluigi Contucci & Stefano Ghirlanda, 2007. "Modeling society with statistical mechanics: an application to cultural contact and immigration," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(4), pages 569-578, August.
    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. Crimaldi, Irene & Dai Pra, Paolo & Louis, Pierre-Yves & Minelli, Ida G., 2019. "Synchronization and functional central limit theorems for interacting reinforced random walks," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 70-101.
    2. Biondi, Yuri & Giannoccolo, Pierpaolo & Galam, Serge, 2012. "Formation of share market prices under heterogeneous beliefs and common knowledge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5532-5545.
    3. Galam, Serge, 2010. "Public debates driven by incomplete scientific data: The cases of evolution theory, global warming and H1N1 pandemic influenza," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3619-3631.
    4. Ausloos, Marcel & Nedic, Olgica & Dekanski, Aleksandar & Mrowinski, Maciej J. & Fronczak, Piotr & Fronczak, Agata, 2017. "Day of the week effect in paper submission/acceptance/rejection to/in/by peer review journals. II. An ARCH econometric-like modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 462-474.
    5. Asad Ur Rehman & Muhammad Shoaib & Mohsin Javed & Zuhair Abbas & Ayesha Nawal & Roman Zámečník, 2022. "Understanding Revisit Intention towards Religious Attraction of Kartarpur Temple: Moderation Analysis of Religiosity," Sustainability, MDPI, vol. 14(14), pages 1-19, July.
    6. Imre Kondor & István Csabai & Gábor Papp & Enys Mones & Gábor Czimbalmos & Máté Sándor, 2014. "Strong random correlations in networks of heterogeneous agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 203-232, October.
    7. Werner Kirsch & Gabor Toth, 2020. "Two Groups in a Curie–Weiss Model with Heterogeneous Coupling," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2001-2026, December.
    8. Galam, Serge, 2011. "Collective beliefs versus individual inflexibility: The unavoidable biases of a public debate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(17), pages 3036-3054.
    9. Michael Fleermann & Werner Kirsch & Gabor Toth, 2022. "Local Central Limit Theorem for Multi-group Curie–Weiss Models," Journal of Theoretical Probability, Springer, vol. 35(3), pages 2009-2019, September.
    10. Ferrari, Mascia & Fedele, Micaela & Luzi, Rachele & Vernia, Cecilia, 2025. "A statistical mechanics approach to measure peer-to-peer effects in Pharma research and development investments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    11. Francesco Camilli & Emanuele Mingione & Godwin Osabutey, 2025. "Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model," Mathematics, MDPI, vol. 13(8), pages 1-25, April.
    12. Rickard Sandell & Pierluigi Contucci, 2015. "How integrated are immigrants?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(46), pages 1271-1280.
    13. Pierluigi Contucci & János Kertész & Godwin Osabutey, 2022. "Human-AI ecosystem with abrupt changes as a function of the composition," PLOS ONE, Public Library of Science, vol. 17(5), pages 1-12, May.

    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:plo:pone00:0339060. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.