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A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network OXn, silicate network SLn, chain silicate network CSn, and hexagonal network HXn. Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network HCn.