  We calculate the most divergent contribution to the non-degenerate sector of
the self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FK
Spin Foam model of Quantum Gravity. We find that such a contribution is
logarithmically divergent in the cut-off over the SU(2)-representation spins
when one chooses the face amplitude guaranteeing the face-splitting invariance
of the foam.We also find that the dependence on the boundary data is different
from that of the bare propagator. This fact has its origin in the
non-commutativity of the EPRL-FK Y-map with the projector onto
SL(2,C)-invariant states. In the course of the paper, we discuss in detail the
approximations used during the calculations, its geometrical interpretation as
well as the physical consequences of our result.
