  On finite metric graphs we consider Laplace operators, subject to various
classes of non-self-adjoint boundary conditions imposed at graph vertices. We
investigate spectral properties, existence of a Riesz basis of projectors and
similarity transforms to self-adjoint Laplacians. Among other things, we
describe a simple way how to relate the similarity transforms between
Laplacians on certain graphs with elementary similarity transforms between
matrices defining the boundary conditions.
