This article presents a comprehensive topological analysis of Mostar-type indices and entropy measures applied to Silicon Dioxide \((SiO_{2})\) and nanostructures. To characterize the complexity and variety within \(SiO_{2}\) and other nanostructures, this research looks into the calculation of Mostar-type indices, a unique mathematical framework, and entropy metrics. This work presents a thorough investigation of the atomic arrangements and information content inherent in these materials by using cutting-edge computational tools and algorithms. The measurement of complex molecular structures can be achieved through the correlation of entropy with graphs. Various graph entropies have been proposed in the literature. This study introduces novel graph entropies that utilize bond additive indices to assess network and graph peripherality. Specifically, we calculated the Mostar type indices, Mostar entropy, edge Mostar entropy, and total Mostar entropy for molecular structures such as \(SiO_{2}\) , \(C_{8}\) layer structure, and melem chain nanostructure. Moreover, analytical expressions for these entropies were derived using the cut method.
