This study demonstrates the effectiveness of the \(\delta\) -Sombor index—a refined graph-theoretical descriptor—for the topological characterization and Quantitative Structure-Property Relationship (QSPR) modeling of Metal-Organic Frameworks (MOFs). We derived explicit analytical formulas for the \(\delta\) -Sombor index of two representative coordination systems: a Zn(II)-isophthalate-Dptztz framework and a Nd(III)-Hepna coordination polymer. Furthermore, a comprehensive QSPR analysis was performed on a diverse set of fifty organic linkers. The \(\delta\) -Sombor index exhibited strong correlations with key physicochemical properties—including partition coefficient (logP), molar refractivity (MR), topological polar surface area (tPSA), and solubility (LogS)—as validated through linear, polynomial, and ridge regression models. The high sensitivity of the \(\delta\) -Sombor index to subtle variations in atomic connectivity and coordination geometry underscores its utility as a robust predictive tool for understanding and designing framework materials in which pore geometry and connectivity govern inclusion phenomena. Our findings confirm its significant potential for accelerating the rational design of MOFs with tailored supramolecular host properties, thereby bridging graph theory with the chemistry of molecular inclusion.
