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

Abstract

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.

Keywords

• Ricci flow
• Forman curvature
• complex systems
• dynamic networks
• change detection
• peer-to-peer network