Heider balance under disordered triadic interactions

The Heider balance addresses three-body interactions with the assumption that triads are equally important in dynamics of network. In many networks, relations do not have same strength, so differently weighted. Now, question is how social networks evolve to reduce number unbalanced triangles when they weighted? Are results foreseeable based on what we already learned from unweighted balance? To find solution, consider a fully connected network which assigned different random weights. Weights coming Gaussian probability distribution mean $\ensuremath{\mu}$ and variance $\ensuremath{\sigma}$. We study this system two regimes: (I) ratio $\frac{\ensuremath{\mu}}{\ensuremath{\sigma}}\ensuremath{\ge}1$ corresponds weak disorder (small variance) triads' weight approximately same; (II) $\frac{\ensuremath{\mu}}{\ensuremath{\sigma}}<1$ counts for strong (big weights remarkably diverse. Investigating structural evolution such our intention. see plays key role determining critical temperature system. Using mean-field method present an analytic solution represents undergoes first-order phase transition. For disorder, simulation display reaches global minimum as decreases, whereas second regime, due diversity weights, does manage reach minimum.