  This article reports on how diagrammatic identities of Yang--Mills theory
translate to diagrammatics for pure gravity. For this, we consider the
Einstein--Hilbert action and follow the approach of Capper, Leibbrandt, and
Medrano and expand the inverse metric density around the Minkowski metric. By
analogy to Yang--Mills theory, cancellation identities are constructed for the
graviton as well as the ghost vertices up to the valency of six.
