Effects of relative homophily and relative heterophily on opinion dynamics in coevolving networks

Opinion dynamics and network topology have received considerable attention. More recently, a growing number of researchers have considered the dynamics of opinions on coevolving networks instead of on static networks. We present an individual preference model in a social network whose initial topology is a directed graph with small-world properties: agents synchronously each select a neighbor to unidirectionally visit and average the opinions between them and their respective neighbors. Guided by a preference for either relative homophily or heterophily, an agent probabilistically visits one of her neighbors, severs the connection, and subsequently, with some probability, rewires a link to a neighbor of that initial neighbor. Moreover, we perform the widely used agent-based computational modeling and simulation to study opinion dynamics and the network structure evolution. We have shown that opinions in some simulations can directly come to an agreement and in other simulations, they have to experience both stabilization process and consensus process. As conservatism increases, stabilization slows down, and the consensus probability decreases. In our model, relative homophily mitigates the clustering phenomenon and ensures that all agents always reach an agreement, while relative heterophily significantly increases the consensus probability in the stabilized state. Furthermore, the social network in our article eventually displays characteristics that are similar to those of scale-free networks and serendipity plays a part in the creation of opinion leaders. Even if the so-called opinion leader ceases to voice opinions or exits the social network, all agents in the network remain capable of achieving consensus.