Opinion dynamics on directed complex networks

TL;DR

This paper introduces a generalized mathematical model for opinion dynamics on directed networks, analyzing how opinions evolve and reach consensus or polarization, influenced by network structure and agent attributes.

Contribution

It extends existing models by incorporating vertex attributes and provides detailed analysis on opinion behavior in directed random graphs with local weak limits.

Findings

Conditions for stationary opinion distribution established

Mechanisms for consensus and polarization explained

Impact of stubborn agents on opinion formation analyzed

Abstract

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.