  When it comes to the mathematical modelling of social interaction patterns, a
number of different models have emerged and been studied over the last decade,
in which individuals randomly interact on the basis of an underlying graph
structure and share their opinions. A prominent example of the so-called
bounded confidence models is the one introduced by Deffuant et al.: Two
neighboring individuals will only interact if their opinions do not differ by
more than a given threshold $\theta$. We consider this model on the line graph
$\mathbb{Z}$ and extend the results that have been achieved for the model with
real-valued opinions by considering vector-valued opinions and general metrics
measuring the distance between two opinion values. Just as in the univariate
case, there exists a critical value for $\theta$ at which a phase transition in
the long-term behavior takes place.
