Evolution of social power over influence networks containing antagonistic interactions

Abstract Individual social power in the opinion formation process over social influence networks has been under intense scientific investigation. Most related works assume explicitly or implicitly that the interpersonal influence weights are always non-negative. In sharp comparison, we argue that such influence weights can be both positive and negative since there exist various contrasting relationships in real-world social networks. Hence, this article studies the evolution of opinion dynamics and social power on cooperative-competitive networks whose influence structure changes via a reflected appraisal mechanism along a sequence of issue discussions. Of particular focus is on identifying the pathways and effects of social power on shaping public opinions from a graph-theoretic perspective. Then, we propose a dynamic model for the reflected self-appraisal process, which enables us to discuss how the individual social power evolves over sequential issue discussions. By accommodating differential Lyapunov theory, we show the global exponential convergence of the self-appraisal model for almost all network topologies. Finally, we conclude that the self-appraisals and social powers are eventually dependent only on an interpersonal appraisal profile.