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.

Selected Works

Melanie Weber
Melanie Weber
Assistant Professor