Recently, multisite models used for the refinement of neutron diffraction data have suggested that the structure of ice VII is quite unlike that of its ordered counterpart, ice VIII. We investigate the oxygen site disorder by modeling the site displacement, obtained from periodic DFT calculations, as a function of the local hydrogen bond network. Then, using graph invariants to describe hydrogen bond fluctuations in the thermodynamic limit, we perform statistical mechanical calculations using the oxygen site displacement model developed here. We find that the probability distribution of the oxygen atom about its perfect lattice site more closely resembles the < 100 > model rather than the recently suggested < 111 > model, although both models represent a simplification of the actual site distribution. We also find a unimodel distribution for the hydrogen bonded oxygen-oxygen distance and a trimodel distribution for the nearest nonbonded oxygen-oxygen distance with a peak separation of similar to 0.1 angstrom.