Graph morphisms as groupoid actors

We describe proper actors from the underlying groupoid of a graph ‐algebra to another étale groupoid in terms of bisections. This allows to understand graph morphisms and the *‐homomorphisms that they induce more conceptually. More generally, we describe actors from the groupoid model of a groupoid correspondence to any étale groupoid. This also covers the groupoids associated to self‐similar groups and self‐similar graphs, among others.