{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T22:49:35Z","timestamp":1768344575413,"version":"3.49.0"},"reference-count":48,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,12,22]],"date-time":"2023-12-22T00:00:00Z","timestamp":1703203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12075144"],"award-info":[{"award-number":["12075144"]}],"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":["12165014"],"award-info":[{"award-number":["12165014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,12,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect more than two nodes, have thus become a new paradigm in network science. Yet, we are still in lack of models linking network growth and hyperedge expansion, both of which are commonly observable in the real world. Here, we propose a generative hypergraph model by employing the preferential attachment mechanism in both nodes and hyperedge formation. The model can produce bi-heterogeneity, exhibiting scale-free distributions in both hyperdegree and hyperedge size. We provide a mean-field treatment that gives the expression of the two scaling exponents, which agree with the numerical simulations. Our model may help to understand the networked systems showing both types of heterogeneity and facilitate the study of complex dynamics thereon.<\/jats:p>","DOI":"10.1093\/comnet\/cnad048","type":"journal-article","created":{"date-parts":[[2023,12,23]],"date-time":"2023-12-23T03:55:09Z","timestamp":1703303709000},"source":"Crossref","is-referenced-by-count":4,"title":["A generative hypergraph model for double heterogeneity"],"prefix":"10.1093","volume":"12","author":[{"given":"Zhao","family":"Li","sequence":"first","affiliation":[{"name":"School of Physics and Information Technology, Shaanxi Normal University , Xian 710062, P.R. China"}]},{"given":"Jing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Physics and Information Technology, Shaanxi Normal University , Xian 710062, P.R. China"}]},{"given":"Guozhong","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Physics and Information Technology, Shaanxi Normal University , Xian 710062, P.R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0335-466X","authenticated-orcid":false,"given":"Li","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Physics and Information Technology, Shaanxi Normal University , Xian 710062, P.R. China"}]},{"given":"Jiqiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic-Electrical Engineering, Ningxia University , Yinchuan 750021, P.R. China"}]},{"given":"Weiran","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Computer Science, Soochow University , Suzhou 215006, P.R. China"}]}],"member":"286","published-online":{"date-parts":[[2023,12,22]]},"reference":[{"key":"2023122303533230200_cnad048-B1","volume-title":"Networks: An Introduction","year":"2010"},{"key":"2023122303533230200_cnad048-B2","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019 networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"2023122303533230200_cnad048-B3","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":"Barab\u00e1si","year":"1999","journal-title":"Science"},{"key":"2023122303533230200_cnad048-B4","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1137\/20M1355896","article-title":"The why, how, and when of representations for complex systems","volume":"63","author":"Torres","year":"2021","journal-title":"SIAM Rev"},{"key":"2023122303533230200_cnad048-B5","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1038\/35065725","article-title":"Exploring complex networks","volume":"410","author":"Strogatz","year":"2001","journal-title":"Nature"},{"key":"2023122303533230200_cnad048-B6","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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