  The question of spatial locality of electronic correlations beyond GW
approximation is one of the central issues of the famous combination of GW and
dynamical mean field theory, GW+DMFT. In this work, the above question is
addressed directly (for the first time) by performing calculations with and
without assumption of locality of the corresponding diagrams. For this purpose
we use sc(GW+G3W2) approach where the higher order part (G3W2) is evaluated
with fully momentum dependent Green's function G and screened interaction W and
with "local" variant, where the single site approximation is assumed for both G
and W. For all three materials studied in this work (NiO, $\alpha$-Ce, LiFeAs),
we have found the spatial non-locality effects to be strong. For NiO and LiFeAs
they, in fact, are decisive for the proper evaluation of vertex corrections.
The results of this study have direct impact on our understanding of
approximations made in practical implementations of GW+DMFT method, where all
diagrams beyond GW (DMFT part) are assumed to be local. Taking into account the
fact that the first diagrams beyond GW represent the most important
contribution also in GW+DMFT calculations, we conclude that the basic
assumption of GW+DMFT, namely the locality of diagrams evaluated in the DMFT
part, is not as good as it is believed to be.
