  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.
