  Several observations indicate the existence of a latent hyperbolic space
behind real networks that makes their structure very intuitive in the sense
that the probability for a connection is decreasing with the hyperbolic
distance between the nodes. A remarkable network model generating random graphs
along this line is the popularity-similarity optimisation (PSO) model, offering
a scale-free degree distribution, high clustering and the small world property
at the same time. These results provide a strong motivation for the development
of hyperbolic embedding algorithms, that tackle the problem of finding the
optimal hyperbolic coordinates of the nodes based on the network structure. A
very promising recent approach for hyperbolic embedding is provided by the
noncentered minimum curvilinear embedding (ncMCE) method, belonging to the
family of coalescent embedding algorithms. This approach offers a high quality
embedding at a low running time. In the present work we propose 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.
