  We study transport in topologically disordered networks that are subjected to
an environment that induces classical diffusion. The dynamics is
phenomenologically described within the framework of the recently introduced
quantum stochastic walk, allowing to study the crossover between coherent
transport and purely classical diffusion. We find that the coupling to the
environment removes all effects of localization and quickly leads to classical
transport. Furthermore, we find that on the level of the transport efficiency,
the system can be well described by reducing it to a two-node network (a
dimer).
