Soft communities in similarity space

Abstract

The ${\mathbb{S}}^1$ model has been a central geometric model in the development of the field of network geometry. It has been mainly studied in its homogeneous regime, in which angular coordinates are independently and uniformly scattered on the circle. We now investigate if the model can generate networks with targeted topological features and soft communities, that is, heterogeneous angular distributions. Under these circumstances, hidden degrees must depend on angular coordinates and we propose a method to estimate them. We conclude that the model can be topologically invariant with respect to the soft-community structure. Our results might have important implications, both in expanding the scope of the model beyond the independent hidden variables limit and in the embedding of real-world networks.

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• The inherent community structure of hyperbolic networks
• Scaling theory of fractal complex networks
• Emergence of geometric Turing patterns in complex networks
• A geometry-induced topological phase transition in random graphs
• Model-independent methods for embedding directed networks into Euclidean and hyperbolic spaces
• Optimisation of the coalescent hyperbolic embedding of complex networks
• Network Renormalization
• Maximally modular structure of growing hyperbolic networks
• Random graphs and real networks with weak geometric coupling
• Geometric detection of hierarchical backbones in real networks
• Geometric randomization of real networks with prescribed degree sequence
• Community detection in hypergraphs through hyperedge percolation
• Symmetry-driven embedding of networks in hyperbolic space
• Robustness and size-dependence of circadian rhythms in multiscale suprachiasmatic-nucleus networks