  Using a formulation of the post-Newtonian expansion in terms of Feynman
graphs, we discuss how various tests of General Relativity (GR) can be
translated into measurement of the three- and four-graviton vertices. In
problems involving only the conservative dynamics of a system, a deviation of
the three-graviton vertex from the GR prediction is equivalent, to lowest
order, to the introduction of the parameter beta_{PPN} in the parametrized
post-Newtonian formalism, and its strongest bound comes from lunar laser
ranging, which measures it at the 0.02% level. Deviation of the three-graviton
vertex from the GR prediction, however, also affects the radiative sector of
the theory. We show that the timing of the Hulse-Taylor binary pulsar provides
a bound on the deviation of the three-graviton vertex from the GR prediction at
the 0.1% level. For coalescing binaries at interferometers we find that,
because of degeneracies with other parameters in the template such as mass and
spin, the effects of modified three- and four-graviton vertices is just to
induce an error in the determination of these parameters and, at least in the
restricted PN approximation, it is not possible to use coalescing binaries for
constraining deviations of the vertices from the GR prediction.
