{"id":"https://openalex.org/W2766701629","doi":"https://doi.org/10.1109/tkde.2017.2764468","title":"Exploring Triangle-Free Dense Structures","display_name":"Exploring Triangle-Free Dense Structures","publication_year":2017,"publication_date":"2017-10-19","ids":{"openalex":"https://openalex.org/W2766701629","doi":"https://doi.org/10.1109/tkde.2017.2764468","mag":"2766701629"},"language":"en","primary_location":{"id":"doi:10.1109/tkde.2017.2764468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2017.2764468","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008951824","display_name":"Can Lu","orcid":"https://orcid.org/0000-0002-7334-2875"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Can Lu","raw_affiliation_strings":["Chinese University of Hong Kong, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075642293","display_name":"Jeffrey Xu Yu","orcid":"https://orcid.org/0000-0002-9738-827X"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jeffrey Xu Yu","raw_affiliation_strings":["Chinese University of Hong Kong, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0002-9738-827X","affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101579923","display_name":"Hao Wei","orcid":"https://orcid.org/0000-0003-0747-9889"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Hao Wei","raw_affiliation_strings":["Chinese University of Hong Kong, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0003-0747-9889","affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":null,"apc_paid":null,"fwci":0.3005,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.553207,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"30","issue":"2","first_page":"278","last_page":"291"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9861999750137329,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.7830523252487183},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6929799318313599},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5631210803985596},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5300193428993225},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5194036960601807},{"id":"https://openalex.org/keywords/contradiction","display_name":"Contradiction","score":0.516588568687439},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.49100640416145325},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43197986483573914},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1339089572429657},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09621429443359375},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.08126404881477356}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7830523252487183},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6929799318313599},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5631210803985596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5300193428993225},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5194036960601807},{"id":"https://openalex.org/C2776728590","wikidata":"https://www.wikidata.org/wiki/Q363948","display_name":"Contradiction","level":2,"score":0.516588568687439},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.49100640416145325},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43197986483573914},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1339089572429657},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09621429443359375},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.08126404881477356},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tkde.2017.2764468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2017.2764468","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","raw_type":"journal-article"},{"id":"pmh:oai:opus.lib.uts.edu.au:10453/131874","is_oa":false,"landing_page_url":"http://hdl.handle.net/10453/131874","pdf_url":null,"source":{"id":"https://openalex.org/S4306401357","display_name":"UTS ePRESS (University of Technology Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114017466","host_organization_name":"University of Technology Sydney","host_organization_lineage":["https://openalex.org/I114017466"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W950821216","https://openalex.org/W1500383076","https://openalex.org/W1571820319","https://openalex.org/W1572923654","https://openalex.org/W1584510240","https://openalex.org/W1604983895","https://openalex.org/W1875112053","https://openalex.org/W1971421925","https://openalex.org/W1973556323","https://openalex.org/W1981663184","https://openalex.org/W1991306266","https://openalex.org/W1994618970","https://openalex.org/W1997698259","https://openalex.org/W2000042664","https://openalex.org/W2007567227","https://openalex.org/W2008620264","https://openalex.org/W2013414394","https://openalex.org/W2019724001","https://openalex.org/W2022322548","https://openalex.org/W2027377866","https://openalex.org/W2032100393","https://openalex.org/W2037933327","https://openalex.org/W2044881936","https://openalex.org/W2061901927","https://openalex.org/W2085739199","https://openalex.org/W2089458547","https://openalex.org/W2094438284","https://openalex.org/W2100409033","https://openalex.org/W2101267973","https://openalex.org/W2102322109","https://openalex.org/W2107933610","https://openalex.org/W2109469951","https://openalex.org/W2111787123","https://openalex.org/W2112090702","https://openalex.org/W2125050594","https://openalex.org/W2125315567","https://openalex.org/W2130354913","https://openalex.org/W2138621811","https://openalex.org/W2148606196","https://openalex.org/W2151626491","https://openalex.org/W2153624566","https://openalex.org/W2166531833","https://openalex.org/W2169206507","https://openalex.org/W2469279958","https://openalex.org/W2796689370","https://openalex.org/W3098234630","https://openalex.org/W3103362336","https://openalex.org/W3142517368","https://openalex.org/W4232932184","https://openalex.org/W4238452917","https://openalex.org/W4312512934","https://openalex.org/W6629621823","https://openalex.org/W6636143309","https://openalex.org/W6684308506"],"related_works":["https://openalex.org/W2381825231","https://openalex.org/W2377933838","https://openalex.org/W2348916262","https://openalex.org/W4210310594","https://openalex.org/W2330422317","https://openalex.org/W2354224618","https://openalex.org/W2354172502","https://openalex.org/W2391836570","https://openalex.org/W2361796009","https://openalex.org/W2392027916"],"abstract_inverted_index":{"Triadic":[0],"closure":[1],"is":[2],"ubiquitous":[3],"in":[4,100,110,124,181,191,203],"social":[5,234],"networks,":[6],"which":[7,83],"refers":[8],"to":[9,42,62,107,120,228,246,255],"the":[10,45,64,125,182,196],"property":[11],"among":[12],"three":[13,96],"individuals,":[14],"A,":[15],"B,":[16],"and":[17,28,66,146,166,221,224,243],"C,":[18],"such":[19,162],"that":[20],"if":[21,140,154],"there":[22,31,91],"exist":[23,164],"strong":[24,35],"ties":[25],"between":[26,39],"A-B":[27],"A-C,":[29],"then":[30],"must":[32],"be":[33,56],"a":[34,60,69,75,98,101,131,174],"or":[36],"weak":[37],"tie":[38],"B-C.":[40],"Related":[41],"triadic":[43],"closure,":[44],"number":[46],"of":[47,68,95,199],"triangles":[48,201],"has":[49,103],"been":[50],"extensively":[51],"studied":[52],"since":[53],"it":[54,114],"can":[55],"effectively":[57],"used":[58],"as":[59],"metric":[61],"analyze":[63,195],"structure":[65],"function":[67],"network.":[70,178,235],"In":[71,179],"this":[72],"paper,":[73],"from":[74],"different":[76],"viewpoint,":[77],"we":[78,160],"study":[79],"triangle-free":[80],"dense":[81],"structures":[82],"have":[84,117,142,156],"received":[85],"little":[86],"attention.":[87],"We":[88,194,236],"focus":[89],"on$K_{3,3}$where":[90],"are":[92,138,151],"two":[93,136,149],"subsets":[94],"vertices,":[97],"vertex":[99,109,123],"subset":[102,112],"an":[104,118,226,232,251],"edge":[105,119],"connected":[106],"every":[108],"another":[111],"while":[113],"does":[115],"not":[116,152,169,266],"any":[121],"other":[122],"same":[126],"subset.":[127],"Such$K_{n,n}$in":[128],"general":[129],"implies":[130],"philosophy":[132],"contradiction:":[133],"(a)":[134],"Any":[135,148],"individuals":[137,150],"friends":[139,153],"they":[141,155,167],"no":[143],"common":[144,157],"friends,":[145],"(b)":[147],"friends.":[158],"However,":[159],"find":[161,256],"induced$K_{3,3}$does":[163],"frequently,":[165],"do":[168,265],"disappear":[170],"over":[171,173],"time":[172],"real":[175,183,242],"academic":[176],"collaboration":[177],"addition,":[180],"datasets":[184,245],"tested,":[185],"nearly":[186],"all":[187,230],"edges":[188],"appearing":[189],"in$K_{3,3}$appear":[190],"some":[192],"triangles.":[193],"expected":[197],"numbers":[198],"induced$K_{3,3}$and":[200],"($\\Delta$)":[202],"four":[204],"representative":[205],"random":[206,211],"graph":[207,212],"models,":[208],"namely,":[209],"Erd\u0151s-R\u00e9nyi":[210],"model,":[213,216,220,223],"Watts-Strogatz":[214],"small-world":[215],"Barab\u00e1si-Albert":[217],"preferential":[218],"attachment":[219],"configuration":[222],"give":[225],"algorithm":[227],"enumerate":[229],"distinct$K_{3,3}$in":[231],"undirected":[233],"conduct":[237],"extensive":[238],"experiments":[239],"on":[240],"both":[241],"synthetic":[244],"confirm":[247],"our":[248],"findings.":[249],"As":[250],"application,":[252],"such$K_{3,3}$found":[253],"helps":[254],"new":[257],"stars":[258],"collaborated":[259],"by":[260],"well-known":[261],"figures":[262],"who":[263],"themselves":[264],"collaborate.":[267]},"counts_by_year":[{"year":2018,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
