Geometric sampling of networks. (15th July 2022)

• Record Type: Journal Article
• Authors: Barkanass, Vladislav; Jost, Jürgen; Saucan, Emil
• Editors: Hancock, Edwin
• Is Part Of: Journal of complex networks. Volume 10:Number 4(2022)
• Publication Date: 2022-07-15
• Subjects: network sampling -- backbone extraction -- discrete Ricci curvature and flow -- coarse geometry; Numerical analysis -- Periodicals; Computer networks -- Periodicals; Social networks -- Periodicals; 518.05
• DOI: 10.1093/comnet/cnac014
• Languages: English
• ISSNs: 2051-1310

Abstract

Abstract: Motivated by the methods and results of manifold sampling based on Ricci curvature, we propose a similar approach for networks. To this end, we make an appeal to three types of discrete curvature, namely the graph Forman-, full Forman- and Haantjes–Ricci curvatures for edge-based and node-based sampling. The relation between the Ricci curvature of the original manifold and that of a Ricci curvature driven-discretization is studied, and we show that there is a strong connection between the Forman–Ricci curvatures of the resulting network and the Ricci curvature of the given smooth manifold. We also present the results of experiments on real-life networks, as well as for square grids arising in image processing. Moreover, we consider fitting Ricci flows, and we employ them for the detection of networks' backbone.