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Graph theoretical approaches have been proven to be effective in thecharacterization of connected systems, as well as in quantifying theirdysfunction due to perturbation. In this paper, we show the advantage of anon-Euclidean (hyperbolic) representation of networks to identify localconnectivity perturbations and to characterize the induced effects on a largescale. We propose two perturbation scores based on representations of thenetworks in a latent geometric space, obtained through an embedding onto thehyperbolic Poincar\'e disk. We numerically demonstrate that these methods areable to localize perturbations in networks with homogeneous or heterogeneousdegree connectivity. We apply this framework to identify the most perturbedbrain areas in epileptic patients following surgery. This study is conceived inthe effort of developing more powerful tools to represent and analyze brainnetworks, and it is the first to apply geometric network embedding techniquesto the case of epilepsy.

Detecting local perturbations of networks in a latent hyperbolic space