A Binary Homophily Model for Opinion Dynamics

In this paper we propose a discrete time binary model, based on the homophily social mechanism, that dynamically reduces the cognitive dissonance among the agents in a social network. We show that the binary homophily model can drive an initially structurally unbalanced network towards a socially balanced one. In order to characterise non-structurally balanced equilibrium points, we introduce a (V,Σ)-factorization that finds an interesting interpretation in terms of structurally balanced classes, and can be used to investigate the case of 3 classes and to provide a complete analysis of the convergence to the equilibrium for small-size networks.