Opinion Dynamics and Social Power Evolution

Our recent work [28] proposes the DeGroot-Friedkin dynamical model for the analysis4of social influence networks. This dynamical model describes the evolution of self-appraisals in a5group of individuals forming opinions in a sequence of issues. Under a strong connectivity assumption,6the model predicts the existence and semi-global attractivity of equilibrium configurations for self-7appraisals and social power in the group.8In this paper, we extend the analysis of the DeGroot-Friedkin model to two general scenar-9ios where the interpersonal influence network is not necessarily strongly connected and where the10individuals form opinions with reducible relative interactions. In the first scenario, the relative inter-11action digraph is reducible with globally reachable nodes; in the second scenario, the condensation12of the relative interaction digraph has multiple aperiodic sinks. For both scenarios, we provide the13explicit mathematical formulations of the DeGroot-Friedkin dynamics, characterize their equilibrium14points, and establish their asymptotic attractivity properties. This work completes the study of the15DeGroot-Friedkin model with most general social network settings and predicts that, under all pos-16sible interaction topologies, the emerging social power structures are determined by the individuals’17eigenvector centrality scores.18