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Summary
This summary is machine-generated.

Weighted social networks evolve differently under disorder. Strong disorder prevents networks from reaching optimal balance, unlike networks with weak disorder, which achieve balance.

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Area of Science:

  • Social network analysis
  • Statistical physics
  • Complex systems

Background:

  • Heider balance theory assumes equal importance of triads in network dynamics.
  • Real-world networks often have relations of varying strengths, leading to weighted triads.
  • Understanding the evolution of weighted networks under imbalance is crucial.

Purpose of the Study:

  • To investigate the evolution of weighted social networks aiming to reduce unbalanced triangles.
  • To determine if results from unweighted network balance theory are applicable to weighted networks.
  • To analyze the role of disorder in weighted network structural evolution.

Main Methods:

  • Modeling a fully connected network with randomly weighted triads from a Gaussian distribution.
  • Analyzing two regimes: weak disorder (μ/σ≥1) and strong disorder (μ/σ<1).
  • Employing mean-field theory for an analytic solution and conducting simulations.

Main Results:

  • Disorder significantly influences the critical temperature of the system.
  • The system exhibits a first-order phase transition.
  • Weak disorder allows the network to reach a global minimum, while strong disorder hinders this due to diverse weights.

Conclusions:

  • Weighted network evolution differs from unweighted networks, especially under strong disorder.
  • Network structural evolution is critically dependent on the degree of weight disorder.
  • Strong weight diversity prevents weighted networks from achieving the optimal balanced state observed in simpler models.