  We investigate dynamical aspects of the discrete nonlinear Schr\"{o}dinger
equation (DNLS) in finite lattices. Starting from a periodic chain with nearest
neighbor interactions, we insert randomly links connecting distant pairs of
sites across the lattice. Using localized initial conditions we focus on the
time averaged probability of occupation of the initial site as a function of
the degree of complexity of the lattice and nonlinearity. We observe that
selftrapping occurs at increasingly larger values of the nonlinearity parameter
as the lattice connectivity increases, while close to the fully coupled network
limit, localization becomes more preferred. For nonlinearity values above a
certain threshold we find a reentrant localization transition, viz.
localization when the number of long distant bonds is small followed by
delocalization and enhanced transport at intermediate bond numbers while close
to the fully connected limit localization reappears.
