  Using the weak convergence approach to large deviations, we formulate and
prove the large deviation principle (LDP) for W-random graphs in the cut-norm
topology. This generalizes the LDP for Erd\H{o}s-R{\' e}nyi random graphs by
Chatterjee and Varadhan. Furthermore, we translate the LDP for random graphs to
a class of interacting dynamical systems on such graphs. To this end, we
demonstrate that the solutions of the dynamical models depend continuously on
the underlying graphs with respect to the cut-norm and apply the contraction
principle.
