  In this paper we study the recently proposed tensor networks/AdS
correspondence. We found that the Coxeter group is a useful tool to describe
tensor networks in a negatively curved space. Studying generic tensor network
populated by perfect tensors, we find that the physical wave function
generically do not admit any connected correlation functions of local
operators. To remedy the problem, we assume that wavefunctions admitting such
semi-classical gravitational interpretation are composed of tensors close to,
but not exactly perfect tensors. Computing corrections to the connected two
point correlation functions, we find that the leading contribution is given by
structures related to geodesics connecting the operators inserted at the
boundary physical dofs. Such considerations admit generalizations at least to
three point functions. This is highly suggestive of the emergence of the
analogues of Witten diagrams in the tensor network. The perturbations alone
however do not give the right entanglement spectrum. Using the Coxeter
construction, we also constructed the tensor network counterpart of the BTZ
black hole, by orbifolding the discrete lattice on which the network resides.
We found that the construction naturally reproduces some of the salient
features of the BTZ black hole, such as the appearance of RT surfaces that
could wrap the horizon, depending on the size of the entanglement region A.
