  The arrangement of network nodes in hyperbolic spaces has become a widely
studied problem, motivated by numerous results suggesting the existence of
hidden metric spaces behind the structure of complex networks. Although several
methods have already been developed for the hyperbolic embedding of undirected
networks, approaches able to deal with directed networks are still in their
infancy. Here, we propose a framework based on the dimension reduction of
proximity matrices reflecting the network topology, coupled with a general
conversion method transforming Euclidean node coordinates into hyperbolic ones
even for directed networks. While proposing a new measure of proximity, we also
incorporate an earlier Euclidean embedding method in our pipeline,
demonstrating the widespread applicability of our Euclidean-hyperbolic
conversion. Besides, we introduce a dimension reduction technique that maps the
nodes directly into the hyperbolic space with the aim of reproducing a distance
matrix measured on the given (un)directed network. According to mapping
accuracy, graph reconstruction performance and greedy routing score, our
methods are capable of producing high-quality embeddings for several real
networks.
