{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,9]],"date-time":"2026-08-09T15:39:18Z","timestamp":1786289958907,"version":"3.56.0"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T00:00:00Z","timestamp":1755820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62466049"],"award-info":[{"award-number":["62466049"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2025-ZJ-720"],"award-info":[{"award-number":["2025-ZJ-720"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Plan of Qinghai Province","award":["62466049"],"award-info":[{"award-number":["62466049"]}]},{"name":"Science and Technology Plan of Qinghai Province","award":["2025-ZJ-720"],"award-info":[{"award-number":["2025-ZJ-720"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The internal structure of hyperedges has become central to understanding collective dynamics in hypernetworks. This study investigates the impact of hyperedge overlap on network synchronization when hyperedge structures are explicitly considered. We propose a modified hyper-adjacency matrix that captures the internal organization of the hyperedges while preserving the higher-order properties. Using this framework, we examine how non-complete connections within hyperedges influence synchronization as the overlap increases. Our findings reveal clear differences from fully connected hyperedge models. Furthermore, spectral graph theory and numerical simulations confirm that the structural variations induced by overlaps significantly regulate global synchronization. This work extends the theoretical framework of hypernetwork synchronization and highlights the critical role of hyperedge overlaps in shaping the internal hyperedge structure.<\/jats:p>","DOI":"10.3390\/e27090889","type":"journal-article","created":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T13:47:49Z","timestamp":1755870469000},"page":"889","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Effects of Hyperedge Overlap and Internal Structure on Hypernetwork Synchronization Dynamics"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-6665-3061","authenticated-orcid":false,"given":"Hong-Yu","family":"Chen","sequence":"first","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining 810008, China"},{"name":"The State Key Laboratory of Tibetan Intelligence, Xining 810008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9383-1070","authenticated-orcid":false,"given":"Xiu-Juan","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining 810008, China"},{"name":"The State Key Laboratory of Tibetan Intelligence, Xining 810008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0246-2319","authenticated-orcid":false,"given":"Fu-Xiang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining 810008, China"},{"name":"The State Key Laboratory of Tibetan Intelligence, Xining 810008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-9245-5688","authenticated-orcid":false,"given":"Hai-Bing","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining 810008, China"},{"name":"The State Key Laboratory of Tibetan Intelligence, Xining 810008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1038\/s41567-019-0459-y","article-title":"From networks to optimal higher-order models of complex systems","volume":"15","author":"Lambiotte","year":"2019","journal-title":"Nat. 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