<p>Kudriavite (CdBi₂S₄) is an important semiconductor material with promising applications in various technological domains. This paper focuses on the comprehensive topological study of CdBi₂S₄ using graph theoretical modeling techniques. More specifically, the crystal structure of the compound CdBi₂S₄ is modeled via edge partitioning techniques of graph theory by deriving mathematical closed form expressions for certain important irregularity topological indices. This strategy provides a quantitative approach to assessing the heterogeneity and structural complexity of these chemical compounds. The results highlight the significance of irregularity topological indices in predicting material stability, electronic distribution, and molecular interactions. The integration of graph-theoretic principles with material science fosters advancements in optoelectronics, thermoelectrics, photovoltaics, catalysis, and biomedicine, paving the way for the development of next-generation functional materials. The advanced topological analysis presented in this paper highlights the potential of graph-theoretic approaches in material construction, providing valuable tools for optimizing the properties of CdBi₂S₄ compounds in industrial applications.</p>