Social learning community detection with nonlinear interaction

2026-05-29

AI Summary

This work addresses the limitations of traditional community detection methods, which rely on global graph structure and are thus ill-suited for distributed or privacy-sensitive settings. The authors model community partitioning as a symmetry-breaking process in nonlinear opinion dynamics, demonstrating that global graph segmentation can emerge solely from local, privacy-preserving social learning interactions. They establish, for the first time, that signal exchanges at saturation naturally yield sparse cuts and introduce a Score-based Edge Reliability framework grounded in edge reliability to identify ambiguous boundary nodes. Integrating nonlinear opinion dynamics, spectral graph theory, and multi-topic evaluation, they design three decentralized algorithms that achieve accuracy on par with global methods such as Louvain and Leiden on the ABCD benchmark and the Ngogo chimpanzee network, while approaching the theoretical detectability limit of stochastic block models.

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.

Problem

• community detection
• decentralized systems
• privacy-preserving
• social learning
• network partitioning

Innovation

• decentralized community detection
• nonlinear opinion dynamics
• symmetry breaking
• privacy-preserving social learning
• Score-based Edge Reliability