We consider query answering using views on graph databases, i.e. databases structured as edge-labeled graphs. We mainly consider views and queries specified by Regular Path Queries (RPQ). These are queries selecting pairs of nodes in a graph database that are connected via a path whose sequence of edge labels belongs to some regular language. We say that a view V determines a query Q if for all graph databases D, the view image V(D) always contains enough information to answer Q on D. In other words, there is a well defined function from V(D) to Q(D). Our main result shows that when this function is monotone, there exists a rewriting of Q as a Datalog query over the view instance V(D). In particular the rewriting query can be evaluated in time polynomial in the size of V(D). Moreover this implies that it is decidable whether an RPQ query can be rewritten in Datalog using RPQ views.