Let denote the Rado graph and
its automorphism group. We show that any action of
on
by automorphisms which has finitely many orbits is isomorphic to the natural action. Therefore, in a sense, every interpretation of the Rado graph in itself without parameters is trivial. The proof uses a counting argument. As a corollary, every interpretation of the Rado graph in itself without parameters is definably isomorphic or anti-isomorphic to the Rado graph. Also, there is no interpretation of
– the Rado graph with a constant – in
which does not use parameters.