All simple structures with saturated hydrogen bonding (SHB) are classified into eight categories on the basis of the donor and acceptor numbers on the atoms at each end of the hydrogen bonds. Examples from the literature are included where known, along with seven structures investigated as part of this study (five have SHB). Graph-set descriptions of the hydrogen-bond patterns are given for each of these structures and for some selected literature examples. The structures presented are: piperazine (I), morpholinium chloride (II) and iodide (III) [(II) and (III) are not SHB], three 1:1 cocrystals of diols with 1,4-phenylenediamine (PDA) – PDA·1,8-octane diol (IV), PDA·1,10-decane diol (V), and PDA·1,12-dodecane diol (VI) and 6-amino-1-hexanol (VII). This study discusses some structures that show limitations of the graph-set model, along with possible suggestions to cover these limitations. The cocrystalline PDA·aliphatic diol structures may provide details applicable to the structure of self-assembled monolayers of aliphatic thiol molecules on Au(111) surfaces.