  In this paper we study the classification of right-angled Artin groups up to
commensurability. We characterise the commensurability classes of RAAGs defined
by trees of diameter 4. In particular, we prove a conjecture of Behrstock and
Neumann that there are infinitely many commensurability classes. Hence, we give
first examples of RAAGs that are quasi-isometric but not commensurable.
