Coevolutionary networks with homophily and heterophily

We have investigated a simple coevolutionary network model incorporating three processes-changes of opinions, homophily, and heterophily. In this model, each node holds one of G opinions and changes its opinion, as in the voter model. Homophily is the tendency for connections to form between individuals of the same opinions and heterophily is the opposite effect. If there is no heterophily, this model corresponds to the Holme and Newman model [Phys. Rev. E 74, 056108 (2006)]. We show that the behavior of this model without heterophily can be understood in terms of a mean field approximation. We also find that this model with heterophily exhibits topologically complicated behaviors such as the small-world property.