  Spatially embedded networks are shaped by a combination of purely topological
(space-independent) and space-dependent formation rules. While it is quite easy
to artificially generate networks where the relative importance of these two
factors can be varied arbitrarily, it is much more difficult to disentangle
these two architectural effects in real networks. Here we propose a solution to
the problem by introducing global and local measures of spatial effects that,
through a comparison with adequate null models, effectively filter out the
spurious contribution of non-spatial constraints. Our filtering allows us to
consistently compare different embedded networks or different historical
snapshots of the same network. As a challenging application we analyse the
World Trade Web, whose topology is expected to depend on geographic distances
but is also strongly determined by non-spatial constraints (degree sequence or
GDP). Remarkably, we are able to detect weak but significant spatial effects
both locally and globally in the network, showing that our method succeeds in
retrieving spatial information even when non-spatial factors dominate. We
finally relate our results to the economic literature on gravity models and
trade globalization.
