Opinion Dynamics in Social Networks with Heterogeneous Relationships

Abstract

Recently, significant attention has been devoted to the models of opinion dynamics, which are on the hypothesis of homogeneous relationships. However, many realistic social networks display a large heterogeneity in the relationships of individuals, which have signed and weighted properties. In this paper, we propose a model of opinion dynamics in a network with heterogeneous relationships, where the influence of individuals depends on their heterogeneous relationships. By conducting a series of simulations in different complex social networks, we find that the distribution of opinions at steady state depends on the ratio of number of positive relationships and average connectivity of a network. The final opinions undergo a transition from the bipolarization phase to the consensus phase gradually as increasing the ratio of positive relationships. We also observe that the topological properties of complex networks such as short path length, high clustering, and heterogeneous degrees have few effects on the opinion dynamics at steady state. As to the effects of initial opinion distribution on opinion dynamics, it only makes sense when the social system is full of positive relationships.