Mixed Hegselmann-Krause Dynamics on infinite graphs

TL;DR

This paper extends the mixed Hegselmann-Krause opinion dynamics model to infinite graphs, analyzing conditions for stability and consensus, thereby broadening understanding of opinion evolution in large or infinite network structures.

Contribution

It introduces the mixed HK model on infinite graphs and investigates stability conditions, expanding prior finite graph studies to infinite network settings.

Findings

Conditions for asymptotic stability identified

Vertices in the same component reach consensus under certain conditions

Model encompasses both HK and Deffuant models on infinite graphs

Abstract

The mixed Hegselmann-Krause (HK) model covers the synchronous Hegselmann-Krause model, the asynchronous Hegselmann-Krause model and the Deffuant model. Previous study~\cite{mHK, mHK2} deals with the mixed HK model on finite graphs. In the study, we discuss the mixed HK model on infinite graphs which also covers the HK model and the Deffuant model on infinite graphs. We investigate conditions under which asymptotic stability holds or any two vertices in the same component approaches each other after some finite time.