# Geometric randomization of real networks with prescribed degree sequence

## TL;DR

This paper presents a geometric randomization model for complex networks that preserves degree sequences and underlying geometric structure, serving as a null model to analyze community structure and geometric effects.

## Contribution

The introduced GR model preserves degree sequences and geometric features without estimating hidden variables, simplifying network randomization and analysis.

## Key findings

- Geometric and topological communities are consistent in real networks.
- Randomized networks show communities due to structural constraints.
- GR model effectively isolates geometric effects in network structure.

## Abstract

We introduce a model for the randomization of complex networks with geometric structure. The geometric randomization (GR) model assumes a homogeneous distribution of the nodes in an underlying similarity space and uses rewirings of the links to find configurations that maximize a connection probability akin to that of the $\mathbb{S}^1$ or $\mathbb{H}^2$ geometric network models. However, GR preserves the original degree sequence, as in the configuration model, thus eliminating the fluctuations of the degree cutoff. Moreover, the model does not require the explicit estimation of hidden degree variables, which restricts the number of free parameters to one, controlling the level of clustering in the rewired network. We illustrate the potential of GR as a null model by investigating the effects on modularity that derive from the flattening of geometric communities in both real and synthetic networks. As a result, we find that for real networks the geometric and topological communities are consistent, while for the randomized counterparts, the topological communities detected are attributable to structural constraints induced by the underlying geometric architecture.