Curvature for Graph Learning

Curvature bridges geometry and topology, using local information to derive global statements. While well-known in a differential topology context, it was recently extended to the domain of graphs. In fact, graphs give rise to various notions of curvature, which differ in expressive power and purpose. We will give a brief overview of curvature in graphs, define some relevant concepts, and show their utility for data science and machine learning applications. In particular, we shall discuss two applications: first, the use of curvature to *distinguish* between different models for synthesising new graphs from some unknown distribution; second, a novel *framework* for defining curvature for hypergraphs, whose structural properties require a more generic setting. We will also describe new applications that are specifically geared towards a treatment by curvature, thus underlining the utility of this concept for data science.

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