Analysis of opinion spreading in homogeneous networks with signed relationships

Abstract

Recently, significant attention has been devoted to opinion dynamics in social networks, in which all the relationships between individuals are assumed as positive ones (i.e. friend, altruism or trust). However, many realistic social networks include negative relationships (i.e. enemy or distrust) as well as positive ones. In order to find the dynamical behavior of opinion spreading in signed networks, we propose a model taking into account the impacts of positive and negative relationships. Based on this model, we analyze the dynamical process and provide a detailed mathematical analysis for identifying the threshold of opinion spreading in homogeneous networks with signed relationships. By performing numerical simulations for the threshold in three different signed networks, we find that the theoretical and numerical results are in good agreement, confirming the correctness of our exact solution.