{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T07:17:52Z","timestamp":1762067872695,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T00:00:00Z","timestamp":1663545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001736","name":"German-Israeli Foundation","doi-asserted-by":"publisher","award":["I-1514-304.6\/2019","1471\/20"],"award-info":[{"award-number":["I-1514-304.6\/2019","1471\/20"]}],"id":[{"id":"10.13039\/501100001736","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["I-1514-304.6\/2019","1471\/20"],"award-info":[{"award-number":["I-1514-304.6\/2019","1471\/20"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Temporal information plays a central role in shaping the structure of a network. In this paper, we consider the impact of an object on network structure over time. More specifically, we use a novel object-based dynamic measure to reflect the extent to which an object that is represented in the network by a vertex affects the topology of the network over time. By way of multigraph and Forman\u2013Ricci flow, we assess the object\u2019s impact on graph weights by comparing two graphs, one in which the object is present and one in which the object is absent. After using a case study to demonstrate the impact of Forman\u2013Ricci flow on the network structure, we apply our measure in a semantic network to assess the effects of a word on the interactions between other words that follow it. In addition, we compare our novel measure to centrality and curvature measures so that we can ascertain the advantages of our measure over ones that already exist.<\/jats:p>","DOI":"10.3390\/axioms11090486","type":"journal-article","created":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T21:47:27Z","timestamp":1663624047000},"page":"486","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Object-Based Dynamics: Applying Forman\u2013Ricci Flow on a Multigraph to Assess the Impact of an Object on The Network Structure"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9641-9380","authenticated-orcid":false,"given":"Haim","family":"Cohen","sequence":"first","affiliation":[{"name":"Department of Cognitive Science, The Hebrew University of Jerusalem, Jerusalem 91905, Israel"},{"name":"The Federmann Center for the Study of Rationality, Jerusalem 91904, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinon","family":"Nachshon","sequence":"additional","affiliation":[{"name":"Department of Cognitive Science, The Hebrew University of Jerusalem, Jerusalem 91905, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anat","family":"Maril","sequence":"additional","affiliation":[{"name":"Department of Cognitive Science, The Hebrew University of Jerusalem, Jerusalem 91905, Israel"},{"name":"Department of Psychology, The Hebrew University of Jerusalem, Jerusalem 91905, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paz M.","family":"Naim","sequence":"additional","affiliation":[{"name":"Department of Cognitive Science, The Hebrew University of Jerusalem, Jerusalem 91905, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00fcrgen","family":"Jost","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"},{"name":"The Santa Fe Institute, Santa Fe, NM 87501, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emil","family":"Saucan","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Braude College, Karmiel 2161002, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-021-87587-z","article-title":"Detecting network anomalies using Forman\u2013Ricci curvature and a case study for human brain networks","volume":"11","author":"Chatterjee","year":"2021","journal-title":"Sci. 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