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Abstract In this research, the star gold structure with beta graphene is thoroughly examined. We mainly focus on computing degree-based topological indices, which provide information about the network’s connectivity and complexity as well as structural features. In addition, we compute an entropy measure to represent the uncertainty, information richness, and degree of unpredictability in the network. Furthermore, this study explores the relationships between topological descriptors and entropy using regression models that are logarithmic, linear, and quadratic. By merging these regression models, we uncover hidden patterns and understand the underlying ideas governing the network’s behaviour. Our findings shed light on the connection between topological indices and entropy. This work improves our understanding of star gold structure dynamics and provides a visual framework for interpreting their behaviour.