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We introduce a model for the randomization of complex networks with geometricstructure. The geometric randomization (GR) model assumes a homogeneousdistribution of the nodes in an underlying similarity space and uses rewiringsof the links to find configurations that maximize a connection probability akinto that of the $\mathbb{S}^1$ or $\mathbb{H}^2$ geometric network models.However, GR preserves the original degree sequence, as in the configurationmodel, thus eliminating the fluctuations of the degree cutoff. Moreover, themodel does not require the explicit estimation of hidden degree variables,which restricts the number of free parameters to one, controlling the level ofclustering in the rewired network. We illustrate the potential of GR as a nullmodel by investigating the effects on modularity that derive from theflattening of geometric communities in both real and synthetic networks. As aresult, we find that for real networks the geometric and topologicalcommunities are consistent, while for the randomized counterparts, thetopological communities detected are attributable to structural constraintsinduced by the underlying geometric architecture.

Geometric randomization of real networks with prescribed degree sequence