Opinion Dynamics on Complex Networks

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This award will advance understanding of how the behaviors of internal and external agents affect the evolution of stochastic dynamic networks. As a particular use case, the PI will examine social network models. It is well recognized that social media platforms, while serving as a legitimate means for individuals to exercise free speech and share diverse views, are also susceptible to internal and external manipulation that may lead to adverse societal outcomes. Using a rigorous mathematical analysis, the models and analyses in this project will study the effects of confirmation bias, media signals, and outside influence through autonomous users, on the evolution of networks of diverse agents. The project will investigate the effects of targeted interventions that either reinforce individuals' current beliefs or expose them to different views. By quantifying the effects of different interventions on the evolution of the network, this award can help institutions, policy makers and organizations to understand the behavior and impact of social media in modern society. In addition to the principal use case of social networks, the results of the project are relevant to a host of dynamically evolving complex networks, such as those describing supply chains. The project team, with expertise in operations researcher and political science, will train graduate students with multidisciplinary perspectives who can contribute to a rigorous examination of important societal issues.This project will provide a robust modeling framework for studying the stationary behavior of Markov chains on directed complex networks via the use of random graph theory and local weak convergence, with the goal of obtaining tractable characterizations of their typical stationary behavior. Theoretical results will describe the stationary distribution of the opinions on the network and will support evaluation of means and variances. Computational aspects of the project include validation of the models on publicly available real-world social network data from various data repositories, as well as experimentation with curated synthetic data produced by widely-used theoretical models. The analysis will characterize the network dynamics and identify model parameters that contribute to the emergence of consensus or polarization. The network model studied includes as special cases the classical DeGroot and Friedkin-Johnsen models, and the investigation will provide mathematical proofs for models that have only been studied empirically to date. Extensions include the study of the original DeGroot model on strongly connected sparse random graphs and the analysis of the opinion model on assortative networks under the semi-sparse regime.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.