  A Wilson loop is defined, in 4-D pure Einstein gravity, as the trace of the
holonomy of the Christoffel connection or of the spin connection, and its
invariance under the symmetry transformations of the action is showed
(diffeomorphisms and local Lorentz transformations). We then compute the loop
perturbatively, both on a flat background and in the presence of an external
source; we also allow some modifications in the form of the action, and test
the action of ``stabilized'' gravity. A geometrical analysis of the results in
terms of the gauge group of the euclidean theory, $SO(4)$, leads us to the
conclusion that the correspondent statistical system does not develope any
configuration with localized curvature at low temperature. This ``non-local''
behavior of the quantized gravitational field strongly contrasts with that of
usual gauge fields. Our results also provide an explanation for the absence of
any invariant correlation of the curvature in the same approximation.
