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The space of directions is a notion of boundary associated to an arbitrarytotally disconnected locally compact group. We explicitly calculate the spaceof directions of a group acting vertex transitively with compact open vertexstabilisers on a locally finite connected hyperbolic graph. These are examplesof groups where techniques from geometric group theory can be generalised fromthe discrete to the non-discrete case. We show the space of directions forthese groups is a discrete metric space. Our results resolve a conjecture ofBaumgartner, M\"oller and Willis in the affirmative.

The space of directions for hyperbolic totally disconnected locally compact groups