  We investigate a class of stochastic partial differential equations of
reaction-diffusion type defined on graphs, which can be derived as the limit of
SPDEs on narrow planar channels. In the first part, we demonstrate that this
limit can be achieved under less restrictive assumptions on the regularity of
the noise, compared to [4]. In the second part, we establish the validity of a
large deviation principle for the SPDEs on the narrow channels and on the
graphs, as the width of the narrow channels and the intensity of the noise are
jointly vanishing.
