Topological indices are graph-theoretically based characteristics that allow for the characterization of a molecular structure's underlying connectivity. Degree-based topological indices have been the subject of substantial research and have been connected to numerous chemical characteristics. Gaining relevance is the study of graph entropy indices as a tool for characterizing structural features and as a gauge of the complexity of the connectivity underneath them. The focus of current research is on substructures like beta graphene (β-GN), that are generated from hexagonal honeycomb graphite lattices. In this study, we investigate R, S and Van topological indices of beta graphene structures by using Shannon's entropy model, we generated the graph-based entropies of these structures.