  We investigate the behavior of the empirical neighbourhood distribution of
marked graphs in the framework of local weak convergence. We establish a large
deviation principle for such families of empirical measures. The proof builds
on Bordenave and Caputo's seminal 2015 paper, and Delgosha and Anantharam's
2019 introduction of BC entropy, relying on combinatorial lemmas that allow one
to construct suitable approximations of measures supported on marked trees.
