Forman-Ricci flow for change detection in large dynamic data sets

Melanie Weber, Jürgen Jost, and Emil Saucan

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Submission date: 28. Mar. 2016 (revised version: November 2016)
Pages: 19
published in: Axioms, 5 (2016) 4, art-no. 26 
DOI number (of the published article): 10.3390/axioms5040026
Bibtex
MSC-Numbers: 68, 94, 52
Keywords and phrases: change detection, dynamic networks, Ricci flow, Forman curvature, complex systems
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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 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.