Detecting local perturbations of networks in a latent hyperbolic embedding space

Abstract

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 Poincaré 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.

References in corpus (2)

• Hyperbolic Geometry of Complex Networks
• Navigability of Complex Networks

Cited by in corpus (4)

• Hyperbolic embedding of brain networks detects regions disrupted by neurodegeneration in Alzheimer's disease
• Geometric representations of brain networks can predict the surgery outcome in temporal lobe epilepsy
• Hyperbolic embedding of brain networks as a tool for epileptic seizures forecasting
• Hyperbolic embedding of multilayer networks