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Updated: Nov 23, 2025

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Expulsion from structurally balanced paradise.

Krzysztof Malarz1, Maciej Wołoszyn1

  • 1Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland.

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|December 31, 2020
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Summary
This summary is machine-generated.

Simulations on a triangular lattice show that structural balance quickly leads to disorder. Unlike previous studies, this lattice topology prevents any form of Heider balance, regardless of system size.

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Area of Science:

  • Social psychology
  • Computational sociology
  • Network science

Background:

  • Heider's balance theory describes social triads' tendency towards balance.
  • Previous simulations on complete graphs showed varying degrees of balance.
  • The impact of lattice topology on structural balance evolution was unexplored.

Purpose of the Study:

  • To investigate structural balance evolution on a triangular lattice.
  • To determine if triangular lattice topology influences the emergence of Heider balance.
  • To analyze the relaxation time and system size dependency.

Main Methods:

  • Simulations of structural balance evolution.
  • Utilized the heat-bath algorithm.
  • Employed a triangular lattice structure.

Main Results:

  • The triangular lattice topology prevents the occurrence of any Heider balance.
  • Systems evolved from a balanced state to an unbalanced and disordered state.
  • The system relaxation time was independent of system size.

Conclusions:

  • Triangular lattice topology inherently prevents structural balance.
  • Social systems on this lattice rapidly transition to disorder.
  • Findings contrast with previous studies on complete graphs, highlighting topological effects.