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This study combines structural and coevolutionary balance theories in social networks. It reveals how local and global interactions affect network stability, with a tricritical point influencing phase transitions.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Sociology

Background:

  • Social network balance theory examines structural balance (global link interactions) and coevolutionary balance (local node-link interactions).
  • Structural balance leads to discontinuous phase transitions, while coevolutionary balance results in continuous transitions.

Purpose of the Study:

  • To investigate the combined effects of structural and coevolutionary balance on network stability.
  • To understand how adjusting the robustness of each balance type influences the system's ability to reach a balanced state.

Main Methods:

  • Utilized statistical mechanics methods, including mean-field theory.
  • Employed Monte Carlo numerical simulations to analyze order parameters and system energy.

Main Results:

  • Developed a phase diagram illustrating the competition between structural and coevolutionary balance terms across different ratios and temperatures.
  • Identified a tricritical point where the phase transition shifts from continuous to discrete.
  • Observed local perspective dominance at low temperatures and global perspective dominance at high temperatures.

Conclusions:

  • The interplay between local (coevolutionary) and global (structural) balance significantly impacts network stability.
  • Temperature and the relative robustness of balance terms dictate the nature of phase transitions in social networks.