  We show how to reconstruct a finite directed graph E from its Toeplitz
algebra, its gauge action, and the canonical finite-dimensional abelian
subalgebra generated by the vertex projections. We also show that if E has no
sinks, then we can recover E from its Toeplitz algebra and the generalised
gauge action that has, for each vertex, an independent copy of the circle
acting on the generators corresponding to edges emanating from that vertex. We
show by example that it is not possible to recover E from its Toeplitz algebra
and gauge action alone.
