Why group opinions tend to be converged through continued communication, discussion and interactions? Under the framework of the social influence network model, we rigorously prove that the group consensus is almost surely within finite steps. This is a quite certain result, and reflects the real-world common phenomenon. In addition, we give a convergence time lower bound. Although our explanations are purely based on mathematic deduction, it shows that the latent social influence structure is the key factor for the persistence of disagreement and formation of opinions convergence or consensus in the real world social system.
Keywords: Opinions dynamics; Random graph; Social influence network theory.