Coexistence of opposite opinions in a network with communities

Abstract

The majority rule is applied to a topology that consists of two coupled random networks,thereby mimicking the modular structure observed in social networks. We calculateanalytically the asymptotic behaviour of the model and derive a phase diagram thatdepends on the frequency of random opinion flips and on the inter-connectivity between thetwo communities. It is shown that three regimes may take place: a disorderedregime, where no collective phenomena takes place; a symmetric regime, where thenodes in both communities reach the same average opinion; and an asymmetricregime, where the nodes in each community reach an opposite average opinion. Thetransition from the asymmetric regime to the symmetric regime is shown to bediscontinuous.