  We propose a simple method for resolution of co-spectrality of Schr\"odinger
operators on metric graphs. Our approach consists of attaching a lead to them
and comparing the $S$-functions of the corresponding scattering problems on
these (non-compact) graphs.
  We show that in several cases -- including general graphs on at most 6
vertices, general trees on at most 9 vertices, and general fuzzy balls --
eigenvalues and scattering data are together sufficient to distinguish
co-spectral metric graphs.
