  We define recursion relations for N = 8 supergravity amplitudes using a
generalization of the on-shell diagrams developed for planar N = 4
super-Yang-Mills. Although the recursion relations generically give rise to
non-planar on-shell diagrams, we show that at tree-level the recursion can be
chosen to yield only planar diagrams, the same diagrams occurring in the planar
N = 4 theory. This implies non-trivial identities for non-planar diagrams as
well as interesting relations between the N = 4 and N = 8 theories. We show
that the on-shell diagrams of N = 8 supergravity obey equivalence relations
analogous to those of N = 4 super-Yang-Mills, and we develop a systematic
algorithm for reading off Grassmannian integral formulae directly from the
on-shell diagrams. We also show that the 1-loop 4-point amplitude of N = 8
supergravity can be obtained from on-shell diagrams.
