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