  We prove that Matui's AH conjecture holds for graph groupoids of infinite
graphs. This is a conjecture which relates the topological full group of an
ample groupoid with the homology of the groupoid. Our main result complements
Matui's result in the finite case, which makes the AH conjecture true for all
graph groupoids covered by the assumptions of said conjecture. Furthermore, we
observe that for arbitrary graphs, the homology of a graph groupoid coincides
with the $K$-theory of its groupoid $C^*$-algebra.
