  We consider L-infinity quasi-isomorphisms for Hochschild cochains whose
structure maps admit "graphical expansion". We introduce the notion of stable
formality quasi-isomorphism which formalizes such an L-infinity
quasi-isomorphism. We define a homotopy equivalence on the set of stable
formality quasi-isomorphisms and prove that the set of homotopy classes of
stable formality quasi-isomorphisms form a torsor for the group corresponding
to the zeroth cohomology of the full (directed) graph complex. This result may
be interpreted as a complete description of homotopy classes of formality
quasi-isomorphisms for Hochschild cochains in the "stable setting".
