  We consider the proposal of gr-qc/0508124 for the extraction of the graviton
propagator from the spinfoam formalism. We propose a new ansatz for the
boundary state, using which we can write the propagator as an integral over
SU(2). The perturbative expansion in the Planck length can be recast into the
saddle point expansion of this integral. We compute the leading order and
recover the behavior expected from low-energy physics. In particular, we prove
that the degenerate spinfoam configurations are suppressed.
