Social Learning Community Detection with Nonlinear Interaction

Submitted to Physical Review E

Authors

Anthony Couthures

Athira Jayakumar Varma

Vineeth Satheeskumar Varma

Irinel-Constantin Morărescu

Samson Lasaulce

Antoine Girard

Published

June 2026

Abstract
Conventional community detection requires centralized network data, making it unsuitable for distributed or privacy-preserving systems. In this paper, we demonstrate that macroscopic graph partitioning can emerge purely from strictly local, privacy preserving interactions driven by social learning. By reframing clustering as a symmetry-breaking process within nonlinear opinion dynamics, we show that exchanging saturated state dependent signal (like public actions) forces a network to naturally fracture along its sparsest cuts. We mathematically establish the spectral conditions under which dense core communities lock into stable, polarized states, robustly resisting external influence. To apply this mechanism, we propose three decentralized algorithms, leading up to the Score-based Edge Reliability (SER) framework. By evaluating network ties across multiple independent discussion topics, SER statistically bypasses the errors of traditional greedy bisections and naturally isolates structurally ambiguous frontier nodes. Validations on the ABCD benchmark and the real-world Ngogo chimpanzee network confirm that our fully decentralized approach matches the accuracy of globally optimized heuristics (e.g., Louvain, Leiden) up to a theoretical limit of detectable graphs.

Simulator Demo Paper PDF Preprint GitHub DOI

All publications

Citation

BibTeX citation:
@misc{couthures2026,
  author = {Couthures, Anthony and Jayakumar Varma, Athira and
    Satheeskumar Varma, Vineeth and Morărescu, Irinel-Constantin and
    Lasaulce, Samson and Girard, Antoine},
  title = {Social {Learning} {Community} {Detection} with {Nonlinear}
    {Interaction}},
  date = {2026-06},
  url = {https://anthonycouthures.github.io/publications/2026_preprint_social-learning-community-detection.html},
  doi = {10.48550/arXiv.2606.00268},
  langid = {en},
  abstract = {Conventional community detection requires centralized
    network data, making it unsuitable for distributed or
    privacy-preserving systems. In this paper, we demonstrate that
    macroscopic graph partitioning can emerge purely from strictly
    local, privacy preserving interactions driven by social learning. By
    reframing clustering as a symmetry-breaking process within nonlinear
    opinion dynamics, we show that exchanging saturated state dependent
    signal (like public actions) forces a network to naturally fracture
    along its sparsest cuts. We mathematically establish the spectral
    conditions under which dense core communities lock into stable,
    polarized states, robustly resisting external influence. To apply
    this mechanism, we propose three decentralized algorithms, leading
    up to the Score-based Edge Reliability (SER) framework. By
    evaluating network ties across multiple independent discussion
    topics, SER statistically bypasses the errors of traditional greedy
    bisections and naturally isolates structurally ambiguous frontier
    nodes. Validations on the ABCD benchmark and the real-world Ngogo
    chimpanzee network confirm that our fully decentralized approach
    matches the accuracy of globally optimized heuristics (e.g.,
    Louvain, Leiden) up to a theoretical limit of detectable graphs.}
}
For attribution, please cite this work as:
Anthony Couthures, Athira Jayakumar Varma, Vineeth Satheeskumar Varma, Irinel-Constantin Morărescu, Samson Lasaulce, and Antoine Girard. 2026. “Social Learning Community Detection with Nonlinear Interaction.” arXiv preprint. https://doi.org/10.48550/arXiv.2606.00268.