This contribution examines the interpretation of the Graph Derivative Indices (GDIs) from the Quantum Mechanics (QM) perspective and its relation with the Hückel molecular orbital (HMO) method. The different elements used for calculating Graph Discrete Derivatives over atom-pairs are related to the QM integrals appearing in the Hückel Determinant. The relation between the Coulomb and Resonance Integrals was estimated by the topological way and quantitative values for resonance energies were calculated. Some GDI calculations were performed to the topological interpretation of the aromaticity, expressing the frequencies as probabilities. Starting from topological interpretation for aromaticity, GDI calculations were performed. There is the possibility of expressing the frequencies as probabilities. It allows explaining the atypical formation of cyclobutadiene from the entropic point of view. Considering this hypothesis, experimental resonance energies for 14 molecules were correlated with GDI-topological resonance energies by the same structures. Taking into consideration the regularity and coherence stablished in experiments performed with the GDIs, it is possible to assure that GDIs have interpretations in QM terms.