  Although matter contributions to the graviton self-energy
$-i[\mbox{}^{\mu\nu} \Sigma^{\rho\sigma}](x;x')$ must be separately conserved
on $x^{\mu}$ and ${x'}^{\mu}$, graviton contributions obey the weaker
constraint of the Ward identity, which involves a divergence on both
coordinates. On a general homogeneous and isotropic background this leads to
just four structure functions for matter contributions but nine structure
functions for graviton contributions. We propose a convenient parameterization
for these nine structure functions. We also apply the formalism to explicit one
loop computations of $-i[\mbox{}^{\mu\nu} \Sigma^{\rho\sigma}](x;x')$ on de
Sitter background, one of the contributions from a massless, minimally coupled
scalar and the other for the contribution from gravitons in the simplest gauge.
We also specialize the linearized, quantum-corrected Einstein equation to the
graviton mode function and to the gravitational response to a point mass.
