A method is presented based on graph theory for categorizing hydrogen-bond motifs in such a way that complex hydrogen-bond patterns can be disentangled, or decoded, systematically and consistently. This method is based on viewing hydrogen-bond patterns topologically as if they were intertwined nets with molecules as the nodes and hydrogen bonds as the lines. Surprisingly, very few parameters are needed to define the hydrogen-bond motifs comprising these networks. The methods for making these assignments, and examples of their chemical utility are given.