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Ricci flow is a tool for deforming a smooth manifold into a “standard” one within the same homeomorphism class. We introduce a new analogue of Ricci curvature for finite weighted graphs, based on the concept of effective resistance. The corresponding Ricci flow on graphs satisfies many properties shared by Ricci flow on manifolds. I will describe some of the ideas behind this definition, coming from arithmetic geometry, and demonstrate with some examples. I will also mention how Ricci flow on graphs can be applied to the real-world problem of community detection.

More Information: https://ncts.ntu.edu.tw/people_detail.php?gid=453&bgid=7