We explain some models coming from mathematical modelling of social interactions. In these models, vertices of a graph hold an opinion, taking for instance values in [0,1], and interact with their neighbours provided that the opinions they hold do not differ too much. We give some results and present open conjectures for one of these models, namely the Deffuant model.
We then give some rigorous results for two variants, namely the compass model and the averaging process.
The results are based on joint works with Markus Heydenreich and Timo Vilkas. No prerequisites will be assumed.