Protein and protein-water hydrogen bonds shape the conformational energy landscape of G Protein-Coupled Receptors, GPCRs. As numerous static structures of GPCRs have been solved, the important question arises whether GPCR structures and GPCR conformational dynamics could be described in terms of conserved hydrogen-bond networks, and alterations of these hydrogen-bond networks along the reaction coordinate of the GPCR. To enable efficient analyses of the hydrogen-bond networks of GPCRs we implemented graph-based algorithms, and applied these algorithms to static GPCR structures from structural biology, and from molecular dynamics simulations of two opioid receptors. We find that static GPCR structures tend to have a conserved, core hydrogen-bond network which, when protein and water dynamics are included with simulations, extends to comprise most of the interior of an inactive receptor. In an active receptor, the dynamic protein-water hydrogen-bond network spans the entire receptor, bridging all functional motifs. Such an extensive, dynamic hydrogen-bond network might contribute to the activation mechanism of the GPCR.