{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T03:28:33Z","timestamp":1783654113915,"version":"3.55.0"},"reference-count":45,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2016,11,10]],"date-time":"2016-11-10T00:00:00Z","timestamp":1478736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We present a viable geometric solution for the detection of dynamic effects in complex networks. Building on Forman\u2019s 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.<\/jats:p>","DOI":"10.3390\/axioms5040026","type":"journal-article","created":{"date-parts":[[2016,11,10]],"date-time":"2016-11-10T10:51:39Z","timestamp":1478775099000},"page":"26","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets"],"prefix":"10.3390","volume":"5","author":[{"given":"Melanie","family":"Weber","sequence":"first","affiliation":[{"name":"Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany"},{"name":"Department of Mathematics, University of Leipzigt, Augustusplatz 10, 04109 Leipzig, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5258-6590","authenticated-orcid":false,"given":"J\u00fcrgen","family":"Jost","sequence":"additional","affiliation":[{"name":"Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany"},{"name":"Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emil","family":"Saucan","sequence":"additional","affiliation":[{"name":"Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany"},{"name":"Departments of Mathematics and Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of small-world networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Albert","year":"1999","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1103\/RevModPhys.74.47","article-title":"Statistical mechanics of complex networks","volume":"74","author":"Albert","year":"2002","journal-title":"Rev. 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