  The famous question of Mark Kac "Can one hear the shape of a drum?"
addressing the unique connection between the shape of a planar region and the
spectrum of the corresponding Laplace operator can be legitimately extended to
scattering systems. In the modified version one asks whether the geometry of a
vibrating system can be determined by scattering experiments. We present the
first experimental approach to this problem in the case of microwave graphs
(networks) simulating quantum graphs. Our experimental results strongly
indicate a negative answer. To demonstrate this we consider scattering from a
pair of isospectral microwave networks consisting of vertices connected by
microwave coaxial cables and extended to scattering systems by connecting leads
to infinity to form isoscattering networks. We show that the amplitudes and
phases of the determinants of the scattering matrices of such networks are the
same within the experimental uncertainties. Furthermore, we demonstrate that
the scattering matrices of the networks are conjugated by the, so called,
transplantation relation.
