{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T13:51:16Z","timestamp":1767016276872,"version":"3.41.2"},"reference-count":64,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T00:00:00Z","timestamp":1656460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"German-Israeli Foundation","award":["I-1514-304.6\/2019"],"award-info":[{"award-number":["I-1514-304.6\/2019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,6,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>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\u2013Ricci 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\u2013Ricci 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\u2019 backbone.<\/jats:p>","DOI":"10.1093\/comnet\/cnac014","type":"journal-article","created":{"date-parts":[[2022,4,23]],"date-time":"2022-04-23T11:09:53Z","timestamp":1650712193000},"source":"Crossref","is-referenced-by-count":4,"title":["Geometric sampling of networks"],"prefix":"10.1093","volume":"10","author":[{"given":"Vladislav","family":"Barkanass","sequence":"first","affiliation":[{"name":"ORT Braude College of Technology Department of Applied Mathematics, , Snunit St. 51, Karmiel 2161002, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00fcrgen","family":"Jost","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences , Inselstrasse 22, Leipzig 04103, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9033-0828","authenticated-orcid":false,"given":"Emil","family":"Saucan","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, ORT Braude College of Technology , Snunit St. 51, Karmiel 2161002, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,7,15]]},"reference":[{"volume-title":"Metric Structures for Riemannian and Non-Riemannian Spaces","year":"1999","author":"Gromov,","key":"2022071813065820600_B1"},{"key":"2022071813065820600_B2","doi-asserted-by":"crossref","first-page":"391","DOI":"10.2969\/jmsj\/03730391","article-title":"Rough isometries, and combinatorial approximations of geometries of non-compact Riemannian manifolds","volume":"37","author":"Kanai,","year":"1985","journal-title":"J. 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