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Trust and distrust are common in the opinion interactions among agents in social networks, and they are described by the edges with positive and negative weights in the signed digraph, respectively. It has been shown in social psychology that although the opinions of most agents (followers) tend to prevail, sometimes one agent (leader) with a firm stand and strong influence can impact or even overthrow the preferences of followers. This paper aims to analyze how the leader influences the formation of followers opinions in signed social networks. In addition, this paper considers an asynchronous evolution mechanism of trust/distrust level based on opinion difference, in which the trust/distrust level between neighboring agents is portrayed as a nonlinear weight function of their opinion difference, and each agent interacts with the neighbors to update the trust/distrust level and opinion at the times determined by its own will. Based on the related properties of sub-stochastic and super-stochastic matrices, the inequality conditions about positive and negative weights to achieve opinion consensus and polarization are established. Some numerical simulations based on two well-known networks called the ``12 Angry Men network and the Karate Club network are provided to verify the correctness of the theoretical results.
In this paper, we propose a generalized opinion dynamics model (GODM), which can dynamically compute each persons expressed opinion, to solve the internal opinion maximization problem for social trust networks. In the model, we propose a new, reasona
Structural balance theory has been developed in sociology and psychology to explain how interacting agents, e.g., countries, political parties, opinionated individuals, with mixed trust and mistrust relationships evolve into polarized camps. Recent r
We study a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types o
We propose a mathematical model to study coupled epidemic and opinion dynamics in a network of communities. Our model captures SIS epidemic dynamics whose evolution is dependent on the opinions of the communities toward the epidemic, and vice versa.
In contrast with the scalar-weighted networks, where bipartite consensus can be achieved if and only if the underlying signed network is structurally balanced, the structural balance property is no longer a graph-theoretic equivalence to the bipartit