  In the weak field expansion of euclidean quantum gravity, an analysis of the
Wilson loops in terms of the gauge group, $SO(4)$, shows that the correspondent
statistical system does not develope any configuration with localized curvature
at low temperature. Such a ``non-local'' behavior contrasts strongly with that
of usual gauge fields. We point out a possible relation between this result and
those of the numerical simulations of quantum Regge Calculus. We also give a
general quantum formula for the static potential energy of the gravitational
interaction of two masses, which is compatible with the mentioned vacuum
structure.
