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Opinion Dynamics on Directed Complex Networks

Author

Listed:
  • Nicolas Fraiman

    (Department of Statistics and Operations Research, UNC Chapel Hill, Chapel Hill, North Carolina 27599)

  • Tzu-Chi Lin

    (Department of Statistics and Operations Research, UNC Chapel Hill, Chapel Hill, North Carolina 27599)

  • Mariana Olvera-Cravioto

    (Department of Statistics and Operations Research, UNC Chapel Hill, Chapel Hill, North Carolina 27599)

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, for example, 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.

Suggested Citation

  • Nicolas Fraiman & Tzu-Chi Lin & Mariana Olvera-Cravioto, 2025. "Opinion Dynamics on Directed Complex Networks," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 838-870, May.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:2:p:838-870
    DOI: 10.1287/moor.2022.0250
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