We compute the large deviation rate functional in the limit of large time for the current flowing through a finite graph where a boundary driven system of stochastic particles is evolving with a zero-range dynamics. This result has already been obtained in prevoius papers by other authors and with different approaches. Our new approach uses new techniques and illuminate various connections and different perspectives. In particular, we use a variational approach to derive the rate functional by contraction from a level 2.5 large deviations. We use an exact minimization and show that the result has similarities with a non-reversible and non-quadratic resistor network theory. In the case of a finite lattice the variational structure is a discrete version of the continuous one of the macroscopic fluctuation theory, that we recover in the scaling limit of the mesh going to zero. This is a joint result in collaboration with Rosemary Harris, obtained long ago and unpublished; it will be available and public soon.