Coevolution of opinion dynamics on evolving signed appraisal networks

Abstract

In social networks, the expression of various opinions has great influence on appraisal networks that describe the interpersonal influence structures among agents. In this paper, we analyze opinion dynamics on signed appraisal networks, and, in turn, adjust appraisals of agents under the influence of structural balance theory and social psychological distancing. To clarify such a coevolution process, we provide mathematical formulations of the coevolution dynamics, characterize the convergence properties of opinions, and identify potential invariant appraisal structures with all initial states. We predict that the opinions of agents in a sink strongly connected component achieve a state of bipartite consensus exponentially fast, and the corresponding appraisal subnetwork converges to a fully connected structural balance state, which determines the scope of non-sinks’ opinions. Finally, our findings witness their sociological significance in the context of the well-known Krackhardt’s advice network and an empirical voting network.