Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flows

Melanie Weber, Emil Saucan, and Jürgen Jost

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Submission date: 08. Aug. 2016 (revised version: October 2016)
Pages: 31
published in: Journal of complex networks, 5 (2017) 4, p. 527-550 
DOI number (of the published article): 10.1093/comnet/cnw030
Bibtex
MSC-Numbers: 05C82, 05C75, 05C21, 05C10
Keywords and phrases: complex networks, Forman-Ricci Curvature, Ricci flow, Laplacian Flow, Data Mining
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Abstract:
We introduce Forman-Ricci curvature and its corresponding flows as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical introduction and mathematical motivation, we apply the proposed network-analytic methods to static and dynamic complex networks and compare the results with established node-based characteristics. Our work suggests a number of applications for data mining, including denoising and clustering of experimental data, as well as extrapolation of network evolution.