An economic model of friendship and enmity for measuring social balance in networks

We propose a dynamic economic model of networks where agents can be friends or enemies with one another. This is a decentralized relationship model in that agents decide whether to change their relationships so as to minimize their imbalanced triads. In this model, there is a single parameter, which we call social temperature, that captures the degree to which agents care about social balance in their relationships. We show that the global structure of relationship configuration converges to a unique stationary distribution. Using this stationary distribution, we characterize the maximum likelihood estimator of the social temperature parameter. Since the estimator is computationally challenging to calculate from real social network datasets, we provide a simple simulation algorithm and verify its performance with real social network datasets.