  Recently, it became possible to experimentally generate and characterize a
very thin silica system on a substrate which can be basically described as a 2D
random network. The key structural properties, in particular related to the
ring statistics, could be numerically reproduced by performing molecular
dynamics simulations with an appropriately chosen 2D force field. Using a
maximum entropy formulation it is shown that the probability distribution of
the individual rings and triplets can be related to the ring and triplet
energies, respectively, obtained from the simulations. Using additional
Lagrange parameters, the correct average properties of random networks are
guaranteed. In agreement with previous work, based on distributions of
complementary rings and triplets, respectively, one finds a Boltzmann-type
relation albeit with an effective temperature which largely deviates from the
bath temperature. Furthermore, it is shown that the ring and triplet energies
can be estimated based on the properties of their average inner angles. This
calculation supports, on a quantitative level, the previously suggested angle
mismatch theory. It suggests that correlations among adjacent rings originate
from the net mismatch in the inner ring angles in a triplet of rings. By taking
into account an average effect from the surrounding rings of a triplet, an even
better estimate of the correlations can be provided. That approach is also
applied to estimate of the Aboav-Wearie parameter.
