  We show how to reconstruct a graded ample Hausdorff groupoid with
topologically principal neutrally graded component from the ring structure of
its graded Steinberg algebra over any commutative integral domain with 1,
together with the embedding of the canonical abelian subring of functions
supported on the unit space. We deduce that diagonal-preserving ring
isomorphism of Leavitt path algebras implies $C^*$-isomorphism of
$C^*$-algebras for graphs $E$ and $F$ in which every cycle has an exit.
