Abstract: 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 to relate
the similarity transforms between Laplacians on certain graphs
with elementary similarity transforms between matrices defining
the boundary conditions.
This is joint work with Amru Hussein and Petr Siegl
published in the Transactions of the AMS (2014).