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April 24, 2026Mathematical Social SciencesOpen Access

When social networks polarize: On the number of clusters in the Hegselmann–Krause model

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Authors

WVWout de VosTilburg UniversityMGMichel GrabischCharles UniversityARAgnieszka RusinowskaCentre National de la Recherche Scientifique

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Overview

This analysis reveals the impact of bounded confidence on polarization in social networks, suggesting complex dynamics in cluster formation.

Key Points

  • The study aims to investigate how bounded confidence affects polarization and the number of clusters in opinion dynamics.
  • Analytic study of cluster formation within finite agent frameworks.
  • Simulation to assess the likelihood of disintegration of opinion chains.
  • Formal analysis of cluster dynamics in a continuum model.
  • Identified necessary conditions for polarization in small groups (5 and 6 agents).
  • Clarified non-monotonic relationship between cluster count and confidence threshold.
  • Extended analysis technique applicability to longer communication chains.

Cite This Study

Vos et al. (2026) studied this question.

synapsesocial.com/papers/69eb084f553a5433e34b3522https://doi.org/10.1016/j.mathsocsci.2026.102530
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