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Axioms 2016, 5(4), 26; doi:10.3390/axioms5040026

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

Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany
Department of Mathematics, University of Leipzigt, Augustusplatz 10, 04109 Leipzig, Germany
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Departments of Mathematics and Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Current address: Program in Applied and Computational Mathematics, Princeton University, Fine Hall 221, Washington Road, Princeton, NJ 08544, USA.
Author to whom correspondence should be addressed.
Academic Editor: Humberto Bustince
Received: 10 September 2016 / Revised: 26 October 2016 / Accepted: 7 November 2016 / Published: 10 November 2016
(This article belongs to the Special Issue Discrete Geometry and its Applications)
View Full-Text   |   Download PDF [2282 KB, uploaded 10 November 2016]   |  


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. View Full-Text
Keywords: Ricci flow; Forman curvature; complex systems; dynamic networks; change detection; peer-to-peer network Ricci flow; Forman curvature; complex systems; dynamic networks; change detection; peer-to-peer network

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Weber, M.; Jost, J.; Saucan, E. Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets. Axioms 2016, 5, 26.

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