Hydrogen bonds are crucial factors that stabilize a complex ribonucleic acid (RNA) molecule's three-dimensional (3D) structure. Minute conformational changes can result in variations in the hydrogen bond interactions in a particular structure. Furthermore, networks of hydrogen bonds, especially those found in tight clusters, may be important elements in structure stabilization or function and can therefore be regarded as potential tertiary motifs. In this paper, we describe a graph theoretical algorithm implemented as a web server that is able to search for unbroken networks of hydrogen-bonded base interactions and thus provide an accounting of such interactions in RNA 3D structures. This server, COGNAC (COnnection tables Graphs for Nucleic ACids), is also able to compare the hydrogen bond networks between two structures and from such annotations enable the mapping of atomic level differences that may have resulted from conformational changes due to mutations or binding events. The COGNAC server can be accessed at http://mfrlab.org/grafss/cognac.