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.
This is a joint work with Joan Bosa, Roozbeh Hazrat and Aidan Sims.