{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:46:20Z","timestamp":1753875980920,"version":"3.41.2"},"reference-count":52,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T00:00:00Z","timestamp":1719187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20231142"],"award-info":[{"award-number":["BK20231142"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Jiangsu"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Link prediction has always played a crucial role in unveiling the structural patterns and evolutionary rules of networks. However, as research on complex networks has progressed, the limitations of solely exploring low-order structures have become increasingly apparent. The introduction of high-order organizational theories has not only enriched the conceptual framework of network dynamics but also opened new avenues for investigating the mechanisms of network evolution and adaptation. The complexity and richness of high-order networks pose challenges for link prediction. This study introduces two novel approaches to forecast links in higher-order networks. The first one is to predict links directly in higher-order networks (LPHN), which directly predicts missing links within the higher-order network based on its structure; the other one is to predict higher-order links via link prediction in low-order networks(PHLN), which starts by predicting absent links in a low-order network. Subsequently, the inferred low-order structure is employed as a foundation to extrapolate and reconstruct the predicted higher-order network. Upon comparing the higher-order networks generated by both LPHN and PHLN with the original higher-order networks constructed directly from low-order networks, we discovered that the higher-order networks produced by PHLN exhibit greater accuracy and exhibit a more similar scale of giant components to the original higher-order network. Consequently, the PHLN demonstrates enhanced precision in forecasting the structure of higher-order networks while preserving networks\u2019 structural integrity. Moreover, PHLN exhibits superior performance in the context of large-scale and sparsely connected networks.<\/jats:p>","DOI":"10.1093\/comnet\/cnae031","type":"journal-article","created":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T00:56:33Z","timestamp":1723337793000},"source":"Crossref","is-referenced-by-count":0,"title":["Identification of missing higher-order interactions in complex networks"],"prefix":"10.1093","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4458-5843","authenticated-orcid":false,"given":"Chengjun","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Engineering Research Center of Digital Forensics, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Jiangsu Engineering Center of NetworkMonitoring, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"},{"name":"Nanjing University of Information Science and Technology, Wuxi Institute of Technology , 333 Xishan Avenue , Wuxi, Jiangsu 214000, China"},{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CI-CAEET), Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wang","family":"Suxun","sequence":"additional","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Jiangsu Engineering Center of NetworkMonitoring, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"},{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CI-CAEET), Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"School of Software, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4786-4036","authenticated-orcid":false,"given":"Wenbin","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Engineering Research Center of Digital Forensics, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Jiangsu Engineering Center of NetworkMonitoring, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"},{"name":"Nanjing University of Information Science and Technology, Wuxi Institute of Technology , 333 Xishan Avenue , Wuxi, Jiangsu 214000, China"},{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CI-CAEET), Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"School of Software, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peijun","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Jiangsu Engineering Center of NetworkMonitoring, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"},{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CI-CAEET), Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"School of Software, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yadang","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Jiangsu Engineering Center of NetworkMonitoring, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"},{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CI-CAEET), Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"School of Software, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiarui","family":"Gu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Jiangsu Engineering Center of NetworkMonitoring, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"},{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CI-CAEET), Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"School of Software, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengju","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"Jiangsu Engineering Center of NetworkMonitoring, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"},{"name":"Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CI-CAEET), Nanjing University of Information Science and Technology , 219 Ningliu Road , Nanjing 210044, China"},{"name":"School of Software, Nanjing University of Information Science and Technology , 219 Ningliu Road ,Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Liu","sequence":"additional","affiliation":[{"name":"Jiangsu Vocational College of Medicine , 283 Jiefang South Road , Yancheng, Jiangsu 224005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,8,10]]},"reference":[{"key":"2024081100562875400_cnae031-B1","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.physrep.2012.01.007","article-title":"Physical approach to complex systems","volume":"515","author":"Kwapie\u0144","year":"2012","journal-title":"Phys. Rep"},{"key":"2024081100562875400_cnae031-B2","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.ecolind.2018.03.059","article-title":"A comprehensive evaluation model of regional atmospheric environment carrying capacity: Model development and a case study in china","volume":"91","author":"Guo","year":"2018","journal-title":"Ecol. Indicators"},{"key":"2024081100562875400_cnae031-B3","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1007\/s10021-001-0101-5","article-title":"Understanding the complexity of economic, ecological, and social systems","volume":"4","author":"Holling","year":"2001","journal-title":"Ecosystems"},{"key":"2024081100562875400_cnae031-B4","doi-asserted-by":"crossref","first-page":"20170391","DOI":"10.1098\/rsif.2017.0391","article-title":"Complex systems biology","volume":"14","author":"Ma\u2019ayan","year":"2017","journal-title":"J. R. Soc. Interface"},{"key":"2024081100562875400_cnae031-B5","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1080\/00018730601170527","article-title":"Characterization of complex networks: a survey of measurements","volume":"56","author":"Costa","year":"2007","journal-title":"Adv. Phys"},{"key":"2024081100562875400_cnae031-B6","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1016\/j.physa.2010.11.027","article-title":"Link prediction in complex networks: a survey","volume":"390","author":"L\u00fc","year":"2011","journal-title":"Phys. A Stat. Mech. Appl"},{"key":"2024081100562875400_cnae031-B7","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1016\/j.artint.2006.10.002","article-title":"Complex systems: network thinking","volume":"170","author":"Mitchell","year":"2006","journal-title":"Artif. Intell"},{"key":"2024081100562875400_cnae031-B8","doi-asserted-by":"crossref","first-page":"102716","DOI":"10.1016\/j.jnca.2020.102716","article-title":"Applications of link prediction in social networks: a review","volume":"166","author":"Daud","year":"2020","journal-title":"J. Netw. Comput. Appl"},{"key":"2024081100562875400_cnae031-B9","doi-asserted-by":"crossref","first-page":"40321","DOI":"10.1038\/srep40321","article-title":"Drug response prediction as a link prediction problem","volume":"7","author":"Stanfield","year":"2017","journal-title":"Sci. Rep"},{"key":"2024081100562875400_cnae031-B10","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.physa.2015.05.057","article-title":"Prediction in complex systems: The case of the international trade network","volume":"436","author":"Vidmer","year":"2015","journal-title":"Phys. A Stat. Mech. Appl"},{"key":"2024081100562875400_cnae031-B11","first-page":"99","volume-title":"International Conference on Information Technology in Bio-and Medical Informatics","author":"Folino","year":"2012"},{"key":"2024081100562875400_cnae031-B12","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1111\/oik.04655","article-title":"Prediction in ecology: promises, obstacles and clarifications","volume":"127","author":"Maris","year":"2018","journal-title":"Oikos"},{"key":"2024081100562875400_cnae031-B13","doi-asserted-by":"crossref","first-page":"115991","DOI":"10.1016\/j.eswa.2021.115991","article-title":"Link prediction by deep non-negative matrix factorization","volume":"188","author":"Chen","year":"2022","journal-title":"Expert Syst. Appl"},{"key":"2024081100562875400_cnae031-B14","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.comcom.2022.02.002","article-title":"Path extension similarity link prediction method based on matrix algebra in directed networks","volume":"187","author":"Guo","year":"2022","journal-title":"Comput. Commun"},{"key":"2024081100562875400_cnae031-B15","doi-asserted-by":"crossref","first-page":"1296","DOI":"10.1080\/10618600.2022.2163648","article-title":"Link prediction for egocentrically sampled networks","volume":"32","author":"Li","year":"2023","journal-title":"J. Comput. Graph. Stat"},{"key":"2024081100562875400_cnae031-B16","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1126\/science.aad9029","article-title":"Higher-order organization of complex networks","volume":"353","author":"Benson","year":"2016","journal-title":"Science"},{"key":"2024081100562875400_cnae031-B17","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. Phys"},{"key":"2024081100562875400_cnae031-B18","doi-asserted-by":"crossref","first-page":"108149","DOI":"10.1016\/j.sigpro.2021.108149","article-title":"Signal processing on higher-order networks: Livin\u2019on the edge\u2026 and beyond","volume":"187","author":"Schaub","year":"2021","journal-title":"Sign. Process"},{"first-page":"386","year":"2019","author":"Nassar","key":"2024081100562875400_cnae031-B19"},{"key":"2024081100562875400_cnae031-B20","volume":"9","author":"Wang","year":"2020","journal-title":"Understanding music from symbolic representation with higher order networks."},{"key":"2024081100562875400_cnae031-B21","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1093\/bioinformatics\/btaa775","article-title":"Hiscf: leveraging higher-order structures for clustering analysis in biological networks","volume":"37","author":"Hu","year":"2021","journal-title":"Bioinformatics"},{"key":"2024081100562875400_cnae031-B22","doi-asserted-by":"crossref","first-page":"20210564","DOI":"10.1098\/rspa.2021.0564","article-title":"A system model of three-body interactions in complex networks: consensus and conservation","volume":"478","author":"Shang","year":"2022","journal-title":"Proc. R. Soc. A"},{"key":"2024081100562875400_cnae031-B23","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1137\/21M1414024","article-title":"What are higher-order networks?","volume":"65","author":"Bick","year":"2023","journal-title":"SIAM Rev"},{"key":"2024081100562875400_cnae031-B24","doi-asserted-by":"crossref","first-page":"022308","DOI":"10.1103\/PhysRevE.101.022308","article-title":"Random walks on hypergraphs","volume":"101","author":"Carletti","year":"2020","journal-title":"Phys. Rev. E"},{"key":"2024081100562875400_cnae031-B25","doi-asserted-by":"crossref","first-page":"111701","DOI":"10.1016\/j.chaos.2021.111701","article-title":"Higher-order percolation in simplicial complexes","volume":"155","author":"Zhao","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"2024081100562875400_cnae031-B26","doi-asserted-by":"crossref","first-page":"610","DOI":"10.3390\/e24050610","article-title":"Deep link-prediction based on the local structure of bipartite networks","volume":"24","author":"Lv","year":"2022","journal-title":"Entropy"},{"key":"2024081100562875400_cnae031-B27","doi-asserted-by":"crossref","first-page":"bbac562","DOI":"10.1093\/bib\/bbac562","article-title":"Incorporating higher order network structures to improve mirna\u2013disease association prediction based on functional modularity","volume":"24","author":"He","year":"2023","journal-title":"Brief. Bioinf"},{"volume-title":"Understanding complex systems: from networks to optimal higher-order models","year":"2018","author":"Lambiotte","key":"2024081100562875400_cnae031-B28"},{"key":"2024081100562875400_cnae031-B29","doi-asserted-by":"crossref","first-page":"E11221","DOI":"10.1073\/pnas.1800683115","article-title":"Simplicial closure and higher-order link prediction","volume":"115","author":"Benson","year":"2018","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2024081100562875400_cnae031-B30","doi-asserted-by":"crossref","first-page":"3374","DOI":"10.1109\/TKDE.2015.2453956","article-title":"Triadic closure pattern analysis and prediction in social networks","volume":"27","author":"Huang","year":"2015","journal-title":"IEEE Trans. Knowl. Data Eng"},{"key":"2024081100562875400_cnae031-B31","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.physa.2014.10.011","article-title":"Structural link prediction based on ant colony approach in social networks","volume":"419","author":"Sherkat","year":"2015","journal-title":"Phys. A Stat. Mech. Appl"},{"key":"2024081100562875400_cnae031-B32","first-page":"376","volume-title":"Proceedings of the 2012 IEEE\/ACM International Conference on Advances in Social Networks Analysis and Mining","author":"Lichtnwalter","year":"2012"},{"key":"2024081100562875400_cnae031-B33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2516891","article-title":"Social link prediction in online social tagging systems","volume":"31","author":"Chelmis","year":"2013","journal-title":"ACM Trans. Inf. Syst. (TOIS"},{"first-page":"131","year":"2017","author":"Gu","key":"2024081100562875400_cnae031-B34"},{"key":"2024081100562875400_cnae031-B35","article-title":"Link prediction in relational data","volume":"16","author":"Taskar","year":"2003","journal-title":"Adv. Neural Inf. Process. Syst"},{"key":"2024081100562875400_cnae031-B36","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1002\/rsa.3240040303","article-title":"The birth of the giant component","volume":"4","author":"Janson","year":"1993","journal-title":"Random Struct. Algorithms"},{"key":"2024081100562875400_cnae031-B37","doi-asserted-by":"crossref","first-page":"012309","DOI":"10.1103\/PhysRevE.97.012309","article-title":"Stability of a giant connected component in a complex network","volume":"97","author":"Kitsak","year":"2018","journal-title":"Phys. Rev. E"},{"first-page":"798","year":"2006","author":"Al Hasan","key":"2024081100562875400_cnae031-B38"},{"year":"2018","author":"Zhang","key":"2024081100562875400_cnae031-B39"},{"first-page":"1","year":"2019","author":"Samad","key":"2024081100562875400_cnae031-B40"},{"year":"2015","author":"Gao","key":"2024081100562875400_cnae031-B41"},{"key":"2024081100562875400_cnae031-B42","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1023\/A:1013470632383","article-title":"A faster katz status score algorithm","volume":"7","author":"Foster","year":"2001","journal-title":"Comput. Math. Org. Theory"},{"key":"2024081100562875400_cnae031-B43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjb\/e2011-20207-x","article-title":"Link prediction in complex networks: a clustering perspective","volume":"85","author":"Feng","year":"2012","journal-title":"Eur. Phys. J. B"},{"first-page":"65","year":"2020","author":"Yuan","key":"2024081100562875400_cnae031-B44"},{"key":"2024081100562875400_cnae031-B45","doi-asserted-by":"crossref","first-page":"1650120","DOI":"10.1142\/S0129183116501205","article-title":"Prediction of missing links and reconstruction of complex networks","volume":"27","author":"Zhang","year":"2016","journal-title":"Int. J. Modern Phys. C"},{"key":"2024081100562875400_cnae031-B46","doi-asserted-by":"crossref","first-page":"027104","DOI":"10.1103\/PhysRevE.72.027104","article-title":"Community detection in complex networks using extremal optimization","volume":"72","author":"Duch","year":"2005","journal-title":"Phys. Rev. E"},{"key":"2024081100562875400_cnae031-B47","doi-asserted-by":"crossref","first-page":"065103","DOI":"10.1103\/PhysRevE.68.065103","article-title":"Self-similar community structure in a network of human interactions","volume":"68","author":"Guimera","year":"2003","journal-title":"Phys. Rev. E"},{"key":"2024081100562875400_cnae031-B48","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1038\/415141a","article-title":"Functional organization of the yeast proteome by systematic analysis of protein complexes","volume":"415","author":"Gavin","year":"2002","journal-title":"Nature"},{"key":"2024081100562875400_cnae031-B49","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1073\/pnas.98.2.404","article-title":"The structure of scientific collaboration networks","volume":"98","author":"Newman","year":"2001","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2024081100562875400_cnae031-B50","doi-asserted-by":"crossref","first-page":"211281","DOI":"10.1109\/ACCESS.2020.3038791","article-title":"A re-ranking algorithm for identifying influential nodes in complex networks","volume":"8","author":"Yu","year":"2020","journal-title":"IEEE Access"},{"key":"2024081100562875400_cnae031-B51","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.ins.2017.02.003","article-title":"Link prediction in multi-relational networks based on relational similarity","volume":"394","author":"Dai","year":"2017","journal-title":"Inf. Sci"},{"key":"2024081100562875400_cnae031-B52","doi-asserted-by":"crossref","first-page":"127829","DOI":"10.1016\/j.physleta.2021.127829","article-title":"Extreme vulnerability of high-order organization in complex networks","volume":"424","author":"Xia","year":"2022","journal-title":"Phys. Lett. A"}],"container-title":["Journal of Complex Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/comnet\/article-pdf\/12\/4\/cnae031\/58795930\/cnae031.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/comnet\/article-pdf\/12\/4\/cnae031\/58795930\/cnae031.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T00:56:49Z","timestamp":1723337809000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comnet\/article\/doi\/10.1093\/comnet\/cnae031\/7731444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,24]]},"references-count":52,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,6,24]]}},"URL":"https:\/\/doi.org\/10.1093\/comnet\/cnae031","relation":{},"ISSN":["2051-1329"],"issn-type":[{"type":"electronic","value":"2051-1329"}],"subject":[],"published-other":{"date-parts":[[2024,8]]},"published":{"date-parts":[[2024,6,24]]},"article-number":"cnae031"}}