We establish a large deviation principle in a strong topology for the component empirical measure of several sequences of marked random graph models, including Erdos-Renyi random graphs, random regular graphs, and more general configuration models. We show that the corresponding rate function is given by a relatively tractable formula involving the relative entropy functional. We also describe several applications of this result, such as Gibbs conditioning principles. This talk is based on joint work with I-Hsun Chen and Sarath Yasodharan.