Graph networks were formulated, motivated from the structure of molecules, social connections, flow of information, transport systems, and several other physical phenomena’s. New networks are proposed by researchers and its properties are studied for potential application in emerging fields. Inspired by the tiling of the Euclidean plane with hexagons and stare-shaped tiles, we have presented a new network in this research, namely, the Star Hexagon Network. We compute some of the well-known degree based topological indices namely Generalized Zagreb Index, Atom Bond Connectivity Index, Geometric Arithmetic index and other derived indices also for the star hexagon network. The centrality measures of the super cell of the network were also studied.