  Graph theoretical approaches have been proven to be effective in the
characterization of connected systems, as well as in quantifying their
dysfunction due to perturbation. In this paper, we show the advantage of a
non-Euclidean (hyperbolic) representation of networks to identify local
connectivity perturbations and to characterize the induced effects on a large
scale. We propose two perturbation scores based on representations of the
networks in a latent geometric space, obtained through an embedding onto the
hyperbolic Poincar\'e disk. We numerically demonstrate that these methods are
able to localize perturbations in networks with homogeneous or heterogeneous
degree connectivity. We apply this framework to identify the most perturbed
brain areas in epileptic patients following surgery. This study is conceived in
the effort of developing more powerful tools to represent and analyze brain
networks, and it is the first to apply geometric network embedding techniques
to the case of epilepsy.
