  We study the graviton propagator in euclidean loop quantum gravity, using the
spinfoam formalism. We use boundary-amplitude and group-field-theory
techniques, and compute one component of the propagator to first order, under a
number of approximations, obtaining the correct spacetime dependence. In the
large distance limit, the only term of the vertex amplitude that contributes is
the exponential of the Regge action: the other terms, that have raised doubts
on the physical viability of the model, are suppressed by the phase of the
vacuum state, which is determined by the extrinsic geometry of the boundary.
