Social power convergence on duplex influence networks with self-appraisals

This paper explores the evolution of self-appraisals and social power over a sequence of issues to reveal the influence of duplex network structure on opinion dynamics in social networks, where several new findings are available based on the DeGroot-Friedkin model. According to the reflected appraisal mechanism, an agent's self-weight is expressed as the joint effect of his/her social power on both layers, and the mathematical formulations and convergence properties are studied for duplex networks. We find that the self-weights of agents converge to an autocratic configuration on duplex networks with the same star topology on each layer, and establish a democratic system with doubly-stochastic influence matrices where each agent shares uniform social power. The findings demonstrate that the social power of an agent is significantly affected by the involved populations' network topology.