Topological descriptors and Shannon entropy play significant roles in the account of structure and information characteristics of molecular networks. Various degree-based and distance-based topological descriptors are computed to understand the structural peculiarity of the terephthalic tetragonal network. The tetragonal terephthalic compound \((TI_4Te_3Pb)\) is identified based on its distinctive tetragonal crystal structure, consisting of lead (Pb), tellurium (Te) and thallium (Tl). The optically isotropic tetragonal-shaped crystal lattice is axis-centric with a square base and two equal axes and a distinctive third axis (c-axis). Shannon entropy is computed to quantify the uncertainty and information content of the network. Logarithmic regression modeling identifies correlations between calculated indices and entropy, which reveals the mathematical dynamics of these descriptors. Observations are seen to exhibit remarkable connections, indicative of the applicability of logarithmic regression in predicting network attributes. This work adds to the cheminformatics and network theory literature in the suggestion of a systematic approach to the analysis of molecular structures through computation. Furthermore, this work adds to the quantitative structure–property relationship literature through the availability of a dependable computational platform for the analysis of novel nanomaterials, with potential applications in drug discovery, material science, and nanotechnology.
