Intermolecular chemical networks defined by the hydrogen bonds formed at the alpha-quartz vertical bar water interface have been data-mined using graph theoretical methods so as to identify and quantify structural patterns and dynamic behavior. Using molecular-dynamics simulations data, the hydrogen bond (H-bond) distributions for the water-water and water-silanol H-bond networks have been determined followed by the calculation of the persistence of the H-bond, the dipole-angle oscillations that water makes with the surface silanol groups over time, and the contiguous H-bonded chains formed at the interface. Changes in these properties have been monitored as a function of surface coverage. Using the H-bond distribution between water and the surface silanol groups, the actual number of waters adsorbed to the surface is found to be 0.6 H2O/10 angstrom(2), irrespective of the total concentration of waters within the system. The unbroken H-bond network of interfacial waters extends farther than in the bulk liquid; however, it is more fluxional at low surface coverages (i.e., the H-bond persistence in a monolayer of water is shorter than in the bulk) Concentrations of H2O at previously determined water adsorption sites have also been quantified. This work demonstrates the complementary information that can be obtained through graph theoretical analysis of the intermolecular H-bond networks relative to standard analyses of molecular simulation data.