  We theoretically investigate the scattering of few photon light on
Bose-Hubbard lattices using diagrammatic scattering theory. We explicitly
derive general analytical expressions for the lowest order photonic correlation
functions, which we apply numerically to several different lattices. We focus
specifically on non-linear effects visible in the intensity-intensity
correlation function and explain bunching and anti-bunching effects in dimers,
chains, rings and planes. The numerical implementation can be applied to
arbitrary Bose-Hubbard graphs, and we provide it as an attachment to this
publication.
