Neurotransmitter molecules play fundamental roles in neuronal communication and are closely associated with the regulation of cognitive, emotional, and motor functions. Alterations in neurotransmitter-related molecular systems are implicated in various neuropsychiatric and neurodegenerative disorders, underscoring the importance of understanding their structural and physicochemical characteristics. In this study, a graph-theoretic quantitative structure–property relationship (QSPR) framework is developed to investigate the relationships between neurotransmitter molecular structures and selected physicochemical properties using four distance-based topological descriptors: Mostar (Mo), Padmakar–Ivan (PI), Szeged (Sz), and geometric–arithmetic (GA) indices. These descriptors provide mathematically interpretable representations of molecular connectivity, distance relationships, and structural organization. Linear regression models were constructed to examine the relationships between the descriptors and five physicochemical properties, namely molecular weight (MW), polar surface area (PSA), structural complexity (C), solubility (S), and melting point (MP). Model performance was assessed using the coefficient of determination (\(R^2\)), adjusted \(R^2\), root mean square error (RMSE), and actual-versus-fitted value comparisons. The results demonstrate that model fit is strongly property– and descriptor-dependent. The PI descriptor exhibits the strongest regression relationships for MW and C, while Mo provides the strongest model fit for PSA. GA shows the highest relative model fit for solubility among the investigated descriptors, whereas Sz provides the highest relative fit for melting point, although the corresponding linear association remains weak. Overall, the distance-based descriptors provide substantially stronger linear relationships with MW, PSA, and C than with S and MP, indicating that these latter properties are governed by additional structural, conformational, and physicochemical factors that cannot be adequately captured by a single two-dimensional topological descriptor. The findings demonstrate the utility of graph-theoretic descriptors as interpretable tools for preliminary QSPR relationship analysis and provide a basis for future studies incorporating larger and chemically diverse datasets, complementary molecular descriptors, and independent external validation.