Description:

Abstract:

Geometric representations of networks, also known as network embeddings, are routinely used in machine learning, visualization, network science, and graph theory. Network embedding is defined as a mapping of network nodes to points in a suitable latent metric space such that latent distances between connected node pairs are smaller than those between unconnected pairs.

In my talk, I will argue that many real networks, due to their hierarchical structure, are best mapped not into Euclidean spaces, as is often routinely assumed, but to spaces with negative curvature, known as hyperbolic spaces. After a gentle introduction to hyperbolic network geometry, I will discuss the application of hyperbolic network representations to problems of network reconstruction. A paradigmatic example of network reconstruction is the prediction of missing links, where one is interested in identifying unconnected node pairs in a partially observed network that are likely to have missing connections.

I will focus on another problem, which is less studied but is of equal, if not greater, importance: reconstruction of communication paths in an incomplete network. Finding an optimal path is a straightforward task if the network is fully observed. The problem is challenging in situations when a large fraction of network links is unknown, like in a protein interaction network, or when the network is dynamic, like the Internet. I will look into both scenarios and propose applications of path reconstruction to anomaly detection in the interdomain Internet routing and the analysis of biological pathways in protein interaction networks.

Maksim Kitsak, TU Delft

Host: Istvan Kovacs

Keywords: Physics, Astronomy, Complex Systems