© 2020 by SPCTopological indices are numerical parameters of a graph that characterize its molecular topology. In theoretical chemistry, the numerical parameters which are used to depict the molecular topology of graphs are called topological indices. Several physical and chemical properties like boiling point, entropy, heat-formation and vaporization enthalpy of chemical compounds can be determined through these topological indices. Graph theory has a considerable use in evaluating the relation for various topological indices of some derived graphs. In this paper, we studied the general Randić, first Zagreb, ABC, GA, ABC4 and GA5, indices for the Star of David and Hexagonal Cage networks and provided closed formulas of these indices.