Dynamic hydrogen-bond networks provide proteins with structural plasticity required to translate signals such as ligand binding into a cellular response or to transport ions and larger solutes across membranes and, thus, are of central interest to understand protein reaction mechanisms. Here, we present C-Graphs, an efficient tool with graphical user interface that analyzes data sets of static protein structures or of independent numerical simulations to identify conserved, vs unique, hydrogen bonds and hydrogen-bond networks. For static structures, which may belong to the same protein or to proteins with different sequences, C-Graphs uses a clustering algorithm to identify sites of the hydrogen-bond network where waters are conserved among the structures. Using C-Graphs, we identify an internal protein-water hydrogen-bond network common to static structures of visual rhodopsins and adenosine A2A G protein-coupled receptors (GPCRs). Molecular dynamics simulations of a visual rhodopsin indicate that the conserved hydrogen-bond network from static structure can recruit dynamic hydrogen bonds and extend throughout most of the receptor. We release with this work the code for C-Graphs and its graphical user interface.