{"id":"https://openalex.org/W4387133532","doi":"https://doi.org/10.3390/e25101390","title":"Hyper-Null Models and Their Applications","display_name":"Hyper-Null Models and Their Applications","publication_year":2023,"publication_date":"2023-09-28","ids":{"openalex":"https://openalex.org/W4387133532","doi":"https://doi.org/10.3390/e25101390","pmid":"https://pubmed.ncbi.nlm.nih.gov/37895511"},"language":"en","primary_location":{"id":"doi:10.3390/e25101390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101390","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1390/pdf?version=1695902578","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/10/1390/pdf?version=1695902578","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102325378","display_name":"Yujie Zeng","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yujie Zeng","raw_affiliation_strings":["Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000787875","display_name":"Bo Liu","orcid":"https://orcid.org/0000-0002-2802-4405"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bo Liu","raw_affiliation_strings":["Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China"],"raw_orcid":"https://orcid.org/0000-0002-2802-4405","affiliations":[{"raw_affiliation_string":"Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071045573","display_name":"Fang Zhou","orcid":"https://orcid.org/0000-0002-0756-6598"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fang Zhou","raw_affiliation_strings":["Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000969982","display_name":"Linyuan L\u00fc","orcid":"https://orcid.org/0000-0002-2156-0432"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Linyuan L\u00fc","raw_affiliation_strings":["Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China","Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]},{"raw_affiliation_string":"School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou 313001, China","institution_ids":["https://openalex.org/I3018263800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000787875","https://openalex.org/A5000969982"],"corresponding_institution_ids":["https://openalex.org/I126520041","https://openalex.org/I150229711","https://openalex.org/I3018263800"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.9041,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71038541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"25","issue":"10","first_page":"1390","last_page":"1390"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13283","display_name":"Mental Health Research Topics","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/null-model","display_name":"Null model","score":0.8316578269004822},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.8266782760620117},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.6133666038513184},{"id":"https://openalex.org/keywords/null-hypothesis","display_name":"Null hypothesis","score":0.5763891935348511},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5609886050224304},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5124797821044922},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.4563480317592621},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4395107626914978},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3383418321609497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33778589963912964},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.11791658401489258},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09742552042007446},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.09410727024078369},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0803261399269104}],"concepts":[{"id":"https://openalex.org/C36382193","wikidata":"https://www.wikidata.org/wiki/Q7068966","display_name":"Null model","level":2,"score":0.8316578269004822},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.8266782760620117},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.6133666038513184},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.5763891935348511},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5609886050224304},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5124797821044922},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.4563480317592621},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4395107626914978},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3383418321609497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33778589963912964},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.11791658401489258},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09742552042007446},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09410727024078369},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0803261399269104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25101390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101390","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1390/pdf?version=1695902578","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:37895511","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37895511","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10606013","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10606013","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10606013/pdf/entropy-25-01390.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:25b102d30dae48eeb95c71749376e117","is_oa":true,"landing_page_url":"https://doaj.org/article/25b102d30dae48eeb95c71749376e117","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 10, p 1390 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/10/1390/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25101390","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25101390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101390","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1390/pdf?version=1695902578","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","score":0.800000011920929,"display_name":"Good health and well-being"}],"awards":[{"id":"https://openalex.org/G2623300173","display_name":null,"funder_award_id":"2022ZD0211400","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2659616207","display_name":null,"funder_award_id":"T2293771","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5388092984","display_name":null,"funder_award_id":"2023NSFSC1919","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387133532.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1803765581","https://openalex.org/W1995875735","https://openalex.org/W1995907191","https://openalex.org/W2031310794","https://openalex.org/W2040956707","https://openalex.org/W2051510684","https://openalex.org/W2095293504","https://openalex.org/W2100256240","https://openalex.org/W2128366083","https://openalex.org/W2153624566","https://openalex.org/W2167659338","https://openalex.org/W2202347610","https://openalex.org/W2247694002","https://openalex.org/W2800591476","https://openalex.org/W2963912272","https://openalex.org/W3006296570","https://openalex.org/W3033513666","https://openalex.org/W3035258118","https://openalex.org/W3047309339","https://openalex.org/W3106228791","https://openalex.org/W3111258566","https://openalex.org/W3159505179","https://openalex.org/W3176172668","https://openalex.org/W3202715456","https://openalex.org/W4200302993","https://openalex.org/W4214498971","https://openalex.org/W4220689618","https://openalex.org/W4229440440","https://openalex.org/W4235019172","https://openalex.org/W4327928774","https://openalex.org/W4388517109","https://openalex.org/W6755340666","https://openalex.org/W6811022677"],"related_works":["https://openalex.org/W4306992803","https://openalex.org/W2979681497","https://openalex.org/W2378195143","https://openalex.org/W4306992794","https://openalex.org/W2590542766","https://openalex.org/W4306992806","https://openalex.org/W4239137652","https://openalex.org/W4306992821","https://openalex.org/W1999826675","https://openalex.org/W2130815278"],"abstract_inverted_index":{"Null":[0],"models":[1,14,33,53,77,94,128],"are":[2,129],"crucial":[3],"tools":[4],"for":[5,15,34,139,150],"investigating":[6],"network":[7,44,108,157],"topological":[8],"structures.":[9],"However,":[10],"research":[11,146],"on":[12,107,116],"null":[13,32,76,93],"higher-order":[16],"networks":[17],"is":[18],"still":[19],"relatively":[20],"scarce.":[21],"In":[22],"this":[23,145],"study,":[24],"we":[25,49,65,82,100],"introduce":[26],"an":[27],"innovative":[28],"method":[29],"to":[30,70,131],"construct":[31],"hypergraphs,":[35],"namely":[36],"the":[37,72,84,91,96,102,111,154],"hyperedge":[38],"swapping-based":[39],"method.":[40],"By":[41,134],"preserving":[42],"certain":[43],"properties":[45,89],"while":[46],"altering":[47],"others,":[48],"generate":[50],"six":[51],"hyper-null":[52,113,127,143],"with":[54],"various":[55,92,132],"orders":[56],"and":[57,95,118,141,159],"analyze":[58],"their":[59,160],"interrelationships.":[60],"To":[61],"validate":[62],"our":[63,125],"approach,":[64],"first":[66],"employ":[67],"hypergraph":[68,105],"entropy":[69],"assess":[71],"randomness":[73,106],"of":[74,104,153,156],"these":[75],"across":[78],"four":[79],"datasets.":[80],"Furthermore,":[81],"examine":[83],"differences":[85],"in":[86],"important":[87],"statistical":[88],"between":[90],"original":[97],"networks.":[98],"Lastly,":[99],"investigate":[101],"impact":[103],"dynamics":[109],"using":[110],"proposed":[112,126],"models,":[114,144],"focusing":[115],"dismantling":[117],"epidemic":[119],"contagion.":[120],"The":[121],"findings":[122],"show":[123],"that":[124],"applicable":[130],"scenarios.":[133],"introducing":[135],"a":[136],"comprehensive":[137],"framework":[138],"generating":[140],"analyzing":[142],"opens":[147],"up":[148],"avenues":[149],"further":[151],"exploration":[152],"intricacies":[155],"structures":[158],"real-world":[161],"implications.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}