Mixed Hegselmann-Krause Dynamics on infinite graphs

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.