Destructive influence of interlayer coupling on Heider balance in bilayer networks

Area of Science:

• Network Science
• Statistical Physics
• Social Dynamics

Background:

• Heider balance theory explains cognitive consistency in social triads.
• Multilayer networks, where interactions occur across interconnected layers, are increasingly relevant for modeling complex systems.

Purpose of the Study:

• To investigate the impact of interlayer coupling on Heider balance in link multiplex networks.
• To determine how network size and coupling strength influence the emergence of Heider balance.

Main Methods:

• Numerical simulations were employed to model the dynamics of Heider balance.
• Analytical calculations were performed to derive theoretical predictions for balance emergence.
• The study analyzed the effect of varying interlayer coupling strengths and signs.

Main Results:

• Interlayer connections were found to impede the emergence of Heider balance.
• Negative interlayer couplings, analogous to antiferromagnetic interactions, significantly reduce balance.
• The probability of achieving Heider balance decreases with network size (N) as N^(-1/2).

Conclusions:

• Multilayer structures with interlayer coupling can explain the absence of Heider balance in real-world social systems.
• The findings highlight the critical role of network topology and interlayer interactions in social balance phenomena.