Changes in structure and dynamics elicited by agonist ligand binding at the extracellular side of G protein coupled receptors (GPCRs) must be relayed to the cytoplasmic G protein binding side of the receptors. To decipher the role of water-mediated hydrogen-bond networks in this relay mechanism, we have developed graph-based algorithms and analysis methodologies applicable to datasets of static structures of distinct GPCRs. For a reference dataset of static structures of bovine rhodopsin solved at the same resolution, we show that graph analyses capture the internal protein–water hydrogen-bond network. The extended analyses of static structures of rhodopsins and opioid receptors suggest a relay mechanism whereby inactive receptors have in place much of the internal core hydrogen-bond network required for long-distance relay of structural change, with extensive local H-bond clusters observed in structures solved at high resolution and with internal water molecules.