  We investigate Yangian invariance of deformed on-shell diagrams with D=4, N=4
superconformal symmetry. We find that invariance implies a direct relationship
between the deformation parameters and the permutation associated to the
on-shell graph. We analyse the connection with deformations of scattering
amplitudes in N=4 super-Yang-Mills theory and the possibility of using the
deformation parameters as a regulator preserving Yangian invariance. A study of
higher-point tree and loop graphs suggests that manifest Yangian invariance of
the amplitude requires trivial deformation parameters.
