A new approach to the investigation of the proton-disordered structure of clathrate hydrates is presented. This approach is based on topological crystallography. The quotient graphs were built for the unit cells of the cubic structure I and the hexagonal structure H. This is a very convenient way to represent the topology of a hydrogen-bonding network under periodic boundary conditions. The exact proton configuration statistics for the unit cells of structure I and structure H were obtained using the quotient graphs. In addition, the statistical analysis of the proton transfer along hydrogen-bonded chains was carried out.
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