# Community Detection in the Hyperbolic Space

arXiv: https://arxiv.org/abs/1906.09082 · HTML: https://mlsanity.com/paper/1906.09082/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

## Built on by (most cited first, 3 of 3)

- [Exact and rapid linear clustering of networks with dynamic programming](https://mlsanity.com/paper/2301.10403/) (2023)
- [Investigating internal migration with network analysis and latent space representations: An application to Turkey](https://mlsanity.com/paper/2201.03543/) (2022)
- [Leveraging Non-linear Dimension Reduction and Random Walk Co-occurrence for Node Embedding](https://mlsanity.com/paper/2602.24069/) (2026)

## Abstract (arXiv)

Embedding a network in hyperbolic space can reveal interesting features for the network structure, especially in terms of self-similar characteristics. The hidden metric space, which can be thought of as the underlying structure of the network, is able to preserve some interesting features generally observed in real-world networks such as heterogeneity in the degree distribution, high clustering coefficient, and small-world effect. Moreover, the angular distribution of the nodes in the hyperbolic plane reveals a community structure of the embedded network. It is worth noting that, while a large body of literature compares well-known community detection algorithms, there is still no consensus on what defines an ideal community partition on a network. Moreover, heuristics for communities found on networks embedded in the hyperbolic space have been investigated here for the first time. We compare the partitions found on embedded networks to the partitions obtained before the embedding step, both for a synthetic network and for two real-world networks. The second part of this paper presents the application of our pipeline to a network of retweets in the context of the Italian elections. Our results uncover a community structure reflective of the political spectrum, encouraging further research on the application of community detection heuristics to graphs mapped onto hyperbolic planes.