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Summary

This study explores the Heider balance model in random networks, revealing how social relationships transition from order to disorder. It identifies critical factors for predicting phase transitions in complex systems.

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Area of Science:

  • Social network analysis
  • Statistical physics
  • Complex systems theory

Background:

  • Structural balance theory explains social relationship dynamics.
  • The Heider balance model is a key framework for understanding these dynamics.
  • Investigating these models in random graphs is crucial for real-world applicability.

Purpose of the Study:

  • To analyze the Heider balance model's behavior in Erdös-Rényi random graphs.
  • To understand the transition from polarized states to disordered phases in noisy environments.
  • To examine both single-layer and bilayer network configurations.

Main Methods:

  • Development of a mean-field solution for average link polarization.
  • Analysis of structural balance in monolayer and bilayer random networks.
  • Numerical simulations to validate analytical predictions.

Main Results:

  • A first-order phase transition is predicted in the Heider balance model.
  • Critical temperature scaling was determined for monolayer (p^2) and bilayer systems.
  • Specific scaling of interaction strengths (p^-2 for intralayer, p^-1 for interlayer) is required to mimic complete graph dynamics.

Conclusions:

  • The Heider balance model exhibits predictable phase transitions in random graphs.
  • Network density is critical for the accuracy of analytical predictions.
  • The study provides a theoretical framework for understanding social dynamics in complex networks.