Given an infinite connected regular graph , place at each vertex Pois() walkers performing independent lazy simple random walks on simultaneously. When two walkers visit the same vertex at the same time they are declared to be acquainted. We show that when is vertex-transitive and amenable, for all a.s. any pair of walkers will eventually have a path of acquaintances between them. In contrast, we show that when is non-amenable (not necessarily transitive) there is always a phase transition at some . We give general bounds on and study the case that is the -regular tree in more details. Finally, we show that in the non-amenable setup, for every there exists a finite time such that a.s. there exists an infinite set of walkers having a path of acquaintances between them by time .