2022/09/02 by Fraiman, Nicolas, Lin, Tzu-Chi, Olvera-Cravioto, Mariana · 1 citation
#05C80 #60G10 #60J05 #60J85 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Probability (math.PR) #Social and Information Networks (cs.SI)
paper · doi:10.48550/arxiv.2209.00969
We propose and analyze a mathematical model for the evolution of opinions on directed complex networks. Our model generalizes the popular DeGroot and Friedkin-Johnsen models by allowing vertices to have attributes that may influence the opinion dynamics. We start by establishing sufficient conditions for the existence of a stationary opinion distribution on any fixed graph, and then provide an increasingly detailed characterization of its behavior by considering a sequence of directed random graphs having a local weak limit. Our most explicit results are obtained for graph sequences whose local weak limit is a marked Galton-Watson tree, in which case our model can be used to explain a variety of phenomena, e.g., conditions under which consensus can be achieved, mechanisms in which opinions can become polarized, and the effect of disruptive stubborn agents on the formation of opinions.