  If the diffuse extragalactic gamma ray emission traces the large scale
structures of the universe, peculiar anisotropy patterns are expected in the
gamma ray sky. In particular, because of the cutoff distance introduced by the
absorption of 0.1-10 TeV photons on the infrared/optical background, prominent
correlations with the local structures within a range of few hundreds Mpc
should be present. We provide detailed predictions of the signal based on the
PSCz map of the local universe. We also use mock N-body catalogues complemented
with the halo model of structures to study some statistical features of the
expected signatures. The results are largely independent from cosmological
details, and depend mostly on the index of correlation (or bias) of the sources
with respect to the large scale distribution of galaxies. For instance, the
predicted signal in the case of a quadratic correlation (as it may happen for a
dark matter annihilation contribution to the diffuse gamma flux) differs
substantially from a linear correlation case, providing a complementary tool to
unveil the nature of the sources of the diffuse gamma ray emission. The chances
of the present and future space and ground based observatories to measure these
features are discussed.
