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Forman-Ricci flow for change detection in large dynamic data sets
Melanie Weber, Jürgen Jost and Emil Saucan
We present a viable geometric solution for the detection of dynamic effects in complex networks. Building on Forman’s discretization of the classical notion of Ricci curvature, we introduce a novel geometric method to characterize different types of real-world networks with an emphasis on peer-to-peer networks. We study the classical Ricci-flow in a network-theoretic setting and introduce an analytic tool for characterizing dynamic effects. The formalism suggests a novel computational method for change detection and the identification of fast evolving network regions and yields insights into topological properties and the structure of the underlying data.