Reaching Opinion Consensus on Leader–Follower Signed Social Networks With Communication Delays

Consensus is a common opinion evolution phenomenon in social networks. Existing studies generally believe that opinion consensus is easy to reach when the network is connected and only trust relationships exist among agents. Distinguishing from existing studies, this article aims to explore how to reach opinion consensus on leader–follower signed social networks with both trust and distrust relationships among agents. With the help of theoretical tools including binary relation composition and products of nonnegative matrices, the inequality constraints for trust and distrust degrees are established, which ensures that trust relationships can counteract the negative effects of distrust relationships on opinion consensus. In addition, further analysis is conducted on the factors that affect the convergence rate of opinion consensus, including the longest positive distance from leader to the followers as well as the upper bound of communication delays. At last, numerical examples are provided to validate the results.