The trivial case of four water molecules introduces, through demonstration, the cycle reversal procedure. Three types of configurations were created and optimized (Figure The NSNS configuration is lower by about 5kJ/mol in energy than the two others and is the lowest PES minimum for the 4H2O case. Because of the low energy differences between the configurations, the dangling protons are thought to be free to move about and the configurations freely transition between each other. In summary, six PCMs individual PCMs were computed. However, Hydrocycler distinguishes PCMs based on cycles only and does not consider acyclic hydrogens. Furthermore, because of symmetry, the reversal of cycles for the NSNS and NNSS configurations results in the same respective configurations, and the reversal of cycles for the NNNS configuration results in its mirror image. Hence, there are in total only four unique PCMs resulting from optimization and cycle reversal. The four PCMs are members of the same hydrogen bonding family even if their acyclic hydrogens are positioned differently; that is, the configurations have the same signature and therefore generate the same ledger. This is an important observation: several energy minima that vary in acyclic hydrogens may have the same signature since they have the same network graph. Note also that in the four-water case, reversing cycles does not lead to transitions between NSNS, NNSS and NNNS configurations.