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Social dynamics on random graphs show a phase transition from balance to imbalance as social noise increases. This transition depends on graph density and system size, with critical temperatures varying accordingly.

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Area of Science:

  • Social network analysis
  • Statistical physics
  • Computational sociology

Background:

  • Understanding social balance is key to social psychology.
  • Random graph theory provides a framework for modeling complex networks.
  • Social noise, like temperature, can disrupt stable social relations.

Purpose of the Study:

  • To investigate social balance dynamics in random graphs under varying social noise levels.
  • To determine the conditions for phase transitions between balanced and imbalanced social states.
  • To analyze the influence of graph density and system size on these dynamics.

Main Methods:

  • Utilizing classical random graph models.
  • Simulating social interactions with temperature as a proxy for social noise.
  • Analyzing phase transitions and critical phenomena.

Main Results:

  • A smooth crossover or a first-order phase transition to imbalance is observed with increasing social noise.
  • The minimal graph density for a first-order transition decreases with system size (Dmin∝N-0.58(1)).
  • Critical temperature increases with graph density for densities above the minimum threshold (Tc⋆∝D1.719(6)).

Conclusions:

  • Social noise can induce phase transitions in social networks, shifting them from balanced to imbalanced states.
  • Graph density and system size are critical factors determining the nature and conditions of these transitions.
  • The findings offer insights into the stability and evolution of social structures in complex systems.