Discrete Curvature and Machine Learning on Graphs

Complex Networks are popular means for studying a wide variety of systems across the social and natural sciences. In a series of articles, we developed geometric tools to describe the structure and evolution of such networks. The core component of our theory, a discrete Ricci curvature, gives rise to two geometric flows that allow for an edge-based network analysis. Thus we extend the commonly used node-based approach to include edge-based information such as edge weights and directionality for a more comprehensive and computationally efficient characterization of networks.

The analysis of a wide range of complex networks suggests connections between curvature and higher order network structure. As a proxy for local assortativity, curvature identifies long-range connections that act as bridges between major network components. By identifying higher order structural features we characterize and classify the network’s geometry.


Melanie Weber
Melanie Weber
Assistant Professor