  In this paper, we present new expressions for n-point NMHV tree-level gravity
amplitudes. We introduce a method of factorization diagrams which is a simple
graphical representation of R-invariants in Yang-Mills theory. We define the
gravity analogues which we call G-invariants, and expand the NMHV gravity
amplitudes in terms of these objects. We provide explicit formulas of NMHV
gravity amplitudes up to eight points in terms of G-invariants, and give the
general definition for any number of points. We discuss the connection to BCFW
representation, special behavior under large momentum shift, the role of
momentum twistors and the intricate web of spurious poles cancelation. Because
of the close connection between R-invariants and the (tree-level) Amplituhedron
for Yang-Mills amplitudes, we speculate that the new expansion for gravity
amplitudes should correspond to the triangulation of the putative Gravituhedron
geometry.
