Curvature-based Analysis of Complex Networks

Complex networks are a popular means for studying a wide variety of systems across the social and natural sciences and, more recently, representing big data. Recent technological advances allow for a description of these systems on an unprecedented scale. However, due to the immense size and complexity of the resulting networks, efficient evaluation remains a data-analytic challenge.

In a recent series of articles [Weber, Saucan, Jost; J. Complex Networks 2017, 2018], Melanie Weber and her team developed geometric tools for efficiently analyzing the structure and evolution of complex networks. The core component of their theory, a discrete Ricci curvature, translates central tools from differential geometry to the discrete realm. With these tools, they extend the commonly used node-based approach to include edge-based information such as edge weights and directionality for a more comprehensive network characterization. The analysis of a wide range of complex networks suggests connections between curvature and higher order network structure. Their results identify important structural features, including long-range connections of high curvature acting as bridges between major network components. Curvature-based tools allow for an efficient computation of this core structure and, based on this core structure, more expensive analysis, hypothesis testing and learning of complex models becomes more feasible.

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About our speaker:
Melanie Weber is a Ph.D. student at Princeton with an undergraduate degree in math and physics from the University of Leipzig in Germany (where she hails from). Her research interests include (non-Euclidean) geometry and functional analysis, and its applications in machine learning and optimization.

Melanie's Princeton profile:
https://web.math.princeton.edu/~mw25/

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Event Schedule:

• Doors at 6:30 pm (you will go through the lobby and come up to the 3rd floor to complete check-in)
• Talk begins promptly at 7 pm with Q&A
• Networking & Drinks!

Food & beverages will be available.