The network graphs clarify the reaction paths of polymers to isolated units or polymerring structures. Interestingly, the reaction paths from polymer-ring structures to isolated monomers or dimers were rare events compared with the change from polymers to isolated units. This finding is associated with the stabilization of a polymer involving 3-ring formation. Although all the reaction paths in the a-La50 and a-Y50 glasses exhibit very similar probabilities, the probability of reaction from polymer to B3O7 trimer in a-Y50 is less than that in a-La50. The probability of a mutual reaction between a polymers and polymer-ring structures in a-Y50 is higher than that in a-La50. This difference can be attributed to the presence of higher 3-ring contents in the a-Y50 glass compared to a-La50. A comprehensive analysis of the symmetry and shape of each extracted RE coordination structure was undertaken by means of the inertia tensor, spherical harmonics, and Voronoi tessellation analysis. These analyses are now briefly described here.