Abstract
Recent attempts to understand the origin of social fragmentation on the basis of spin models include terms accounting for two social phenomena: homophily-the tendency for people with similar opinions to establish positive relations-and social balance-the tendency for people to establish balanced triadic relations. Spins represent attribute vectors that encode G different opinions of individuals whose social interactions can be positive or negative. Here we present a co-evolutionary Hamiltonian model of societies where people minimise their individual social stresses. We show that societies always reach stationary, balanced, and fragmented states, if-in addition to homophily-individuals take into account a significant fraction, q, of their triadic relations. Above a critical value, [Formula: see text], balanced and fragmented states exist for any number of opinions.