Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets

• Main Authors: Melanie Weber, Jürgen Jost, Emil Saucan
• Format: Article
• Language: English
• Published: MDPI AG 2016-11-01
• Series: Axioms
• Subjects: Ricci flow; Forman curvature; complex systems; dynamic networks; change detection; peer-to-peer network
• Online Access: http://www.mdpi.com/2075-1680/5/4/26

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 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.