  We derive the simplest form of the $\kappa(\kappa^2)$ order graviton
self-interaction Lagrangian density $\lag{1}(\lag{2})$ in the weak field
approximation. With the divergenceless condition, de Donder gauge and some
combinatoric techniques, we derive the mathematically independent basis
expressions for $\lag{1}(\lag{2})$ composed of 8(24) terms. By using the basis
expressions $\lag{1}(\lag{2})$ is reduced to 6(18) terms.
