# Angular separability of data clusters or network communities in geometrical space and its relevance to hyperbolic embedding

@article{Muscoloni2019AngularSO, title={Angular separability of data clusters or network communities in geometrical space and its relevance to hyperbolic embedding}, author={Alessandro Muscoloni and Carlo Vittorio Cannistraci}, journal={ArXiv}, year={2019}, volume={abs/1907.00025} }

Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation of this data derived by real complex physical systems. In the hyperbolic space, the radial coordinate of the nodes characterizes their hierarchy, whereas the angular distance…

## 6 Citations

### Optimisation of the coalescent hyperbolic embedding of complex networks

- Computer ScienceScientific reports
- 2021

This work proposes a further optimisation of the angular coordinates in this framework that seems to reduce the logarithmic loss and increase the greedy routing score of the embedding compared to the original version, thereby adding an extra improvement to the quality of the inferred hyperbolic coordinates.

### Dimension matters when modeling network communities in hyperbolic spaces

- Computer Science
- 2022

It is shown that there is an important qualitativeerence between the lowest-dimensional model and its higher-dimensional counterparts with respect to how similarity between nodes restricts connection probabilities, and considering only one more dimension allows for more realistic and diverse community structures.

### Growing hyperbolic networks beyond two dimensions: the generalised popularity-similarity optimisation model

- Computer Science
- 2021

The dPSO model is introduced, a generalisation of the popularitysimilarity optimisation model to any arbitrary integer dimension d > 2, and shows that their major structural properties can be affected by the dimension of the underlying hyperbolic space in a non-trivial way.

### Generalised popularity-similarity optimisation model for growing hyperbolic networks beyond two dimensions

- Computer ScienceScientific reports
- 2022

The d PSO model is introduced, a generalisation of the popularity-similarity optimisation model to any arbitrary integer dimension $$d>2$$ d > 2 and shows that their major structural properties can be affected by the dimension of the underlying hyperbolic space in a non-trivial way.

### The inherent community structure of hyperbolic networks

- Computer ScienceScientific reports
- 2021

This work extracted the communities from the studied networks using well-established community finding methods such as Louvain, Infomap and label propagation, and observed high modularity values indicate that the community structure can become very pronounced under certain conditions.

### Modular gateway-ness connectivity and structural core organization in maritime network science

- BusinessNature Communications
- 2020

The authors unveiled the architecture of a recent global liner shipping network (GLSN) and show that the structure has evolved to be self-organized with a trade-off between high transportation efficiency and low wiring cost and Ports’ gateway-ness is most highly associated with ports’ economic performance.

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