  Given a Hermitian vector bundle over an infinite weighted graph, we define
the Laplacian associated to a unitary connection on this bundle and study the
essential self-adjointness of a perturbation of this Laplacian by an
operator-valued potential. Additionally, we give a sufficient condition for the
resulting Schr\"odinger operator to serve as the generator of a strongly
continuous contraction semigroup in the corresponding l^{p}-space.
