In this work, interpretable deep learning was used to identify structure-property relationships governing the HOMO-LUMO gap and the relative stability of polybenzenoid hydrocarbons (PBHs) using a ring-based graph representation. This representation was combined with a subunit-based perception of PBHs, allowing chemical insights to be presented in terms of intuitive and simple structural motifs. The resulting insights agree with conventional organic chemistry knowledge and electronic structure-based analyses and also reveal new behaviors and identify influential structural motifs. In particular, we evaluated and compared the effects of linear, angular, and branching motifs on these two molecular properties and explored the role of dispersion in mitigating the torsional strain inherent in nonplanar PBHs. Hence, the observed regularities and the proposed analysis contribute to a deeper understanding of the behavior of PBHs and form the foundation for design strategies for new functional PBHs.