On the one hand, Kontsevich showed that the Lie homology of symplectic vector fields can be computed via a certain graph homology. This has been extended to operads via the work of Conant and Vogtmann. On the other hand, Loday, Quillen and Tsygan have proved that the Lie homology of the Lie matrices can be computed via cyclic homology, which can then be reinterpreted as graph homology. A similar result due to Procesi and Loday has been proven in the orthogonal case. I extend these results to the operadic case by providing funtor from operads to Lie algebras with a group action of one of the groups sp, o, or sl, and relate the Lie homology of these algebras with a graph complex. A generalisation to Leibniz homology gives symmetric graphs.