{"id":"https://openalex.org/W4315489374","doi":"https://doi.org/10.1109/tkde.2022.3232165","title":"Fairness-Aware Maximal Clique in Large Graphs: Concepts and Algorithms","display_name":"Fairness-Aware Maximal Clique in Large Graphs: Concepts and Algorithms","publication_year":2023,"publication_date":"2023-01-10","ids":{"openalex":"https://openalex.org/W4315489374","doi":"https://doi.org/10.1109/tkde.2022.3232165"},"language":"en","primary_location":{"id":"doi:10.1109/tkde.2022.3232165","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2022.3232165","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/A5100360201","display_name":"Qi Zhang","orcid":"https://orcid.org/0000-0001-5841-0350"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qi Zhang","raw_affiliation_strings":["School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100742464","display_name":"Rong-Hua Li","orcid":"https://orcid.org/0000-0001-8658-6599"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rong-Hua Li","raw_affiliation_strings":["School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080285340","display_name":"Minjia Pan","orcid":null},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Minjia Pan","raw_affiliation_strings":["School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102501531","display_name":"Yongheng Dai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongheng Dai","raw_affiliation_strings":["Diankeyun Technologies Ltd, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Diankeyun Technologies Ltd, Beijing, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Qun Tian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qun Tian","raw_affiliation_strings":["Diankeyun Technologies Ltd, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Diankeyun Technologies Ltd, Beijing, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054991337","display_name":"Guoren Wang","orcid":"https://orcid.org/0000-0002-0181-8379"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoren Wang","raw_affiliation_strings":["School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5100360201"],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":2.233,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89875327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"35","issue":"11","first_page":"11368","last_page":"11387"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9905999898910522,"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/T10883","display_name":"Ethics and Social Impacts of AI","score":0.9735999703407288,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.7799626588821411},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.691413938999176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5722702145576477},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5484174489974976},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4752882719039917},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.46642524003982544},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.46198517084121704},{"id":"https://openalex.org/keywords/pruning","display_name":"Pruning","score":0.4588916599750519},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45521870255470276},{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.42501431703567505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3996100425720215},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.35252299904823303},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08855381608009338},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07547134160995483}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.7799626588821411},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.691413938999176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5722702145576477},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5484174489974976},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4752882719039917},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.46642524003982544},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.46198517084121704},{"id":"https://openalex.org/C108010975","wikidata":"https://www.wikidata.org/wiki/Q500094","display_name":"Pruning","level":2,"score":0.4588916599750519},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45521870255470276},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.42501431703567505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3996100425720215},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35252299904823303},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08855381608009338},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07547134160995483},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tkde.2022.3232165","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2022.3232165","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5766186352","display_name":null,"funder_award_id":"62072034","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7835971171","display_name":null,"funder_award_id":"U1809206","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8764403337","display_name":null,"funder_award_id":"U2241211","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W106934005","https://openalex.org/W149461665","https://openalex.org/W248604449","https://openalex.org/W1497191944","https://openalex.org/W1500067272","https://openalex.org/W1546313639","https://openalex.org/W1566772816","https://openalex.org/W1586552957","https://openalex.org/W1594785451","https://openalex.org/W1676999057","https://openalex.org/W1823437338","https://openalex.org/W1970381667","https://openalex.org/W1971717360","https://openalex.org/W1984291654","https://openalex.org/W1987173300","https://openalex.org/W2012921801","https://openalex.org/W2017109153","https://openalex.org/W2046112356","https://openalex.org/W2048653843","https://openalex.org/W2094224753","https://openalex.org/W2100505346","https://openalex.org/W2100960835","https://openalex.org/W2100978151","https://openalex.org/W2106119591","https://openalex.org/W2111315907","https://openalex.org/W2114148358","https://openalex.org/W2116007667","https://openalex.org/W2123963758","https://openalex.org/W2125895010","https://openalex.org/W2151948384","https://openalex.org/W2160429376","https://openalex.org/W2169088933","https://openalex.org/W2183091601","https://openalex.org/W2231297807","https://openalex.org/W2291620117","https://openalex.org/W2320652849","https://openalex.org/W2487826371","https://openalex.org/W2530395818","https://openalex.org/W2547646153","https://openalex.org/W2571329707","https://openalex.org/W2588222785","https://openalex.org/W2604961496","https://openalex.org/W2704480242","https://openalex.org/W2774854434","https://openalex.org/W2788730644","https://openalex.org/W2789635017","https://openalex.org/W2794823917","https://openalex.org/W2809878087","https://openalex.org/W2921273159","https://openalex.org/W2949349735","https://openalex.org/W2950303488","https://openalex.org/W2951813287","https://openalex.org/W2963189767","https://openalex.org/W3012937529","https://openalex.org/W3037117430","https://openalex.org/W3102092462","https://openalex.org/W3102647957","https://openalex.org/W3166231268","https://openalex.org/W4247132858","https://openalex.org/W4283325326","https://openalex.org/W6637459119","https://openalex.org/W6685863130","https://openalex.org/W6696767168","https://openalex.org/W6728551298","https://openalex.org/W6760725079"],"related_works":["https://openalex.org/W4249653852","https://openalex.org/W2789636091","https://openalex.org/W2282273380","https://openalex.org/W4296570398","https://openalex.org/W1498460077","https://openalex.org/W2076040942","https://openalex.org/W2113826940","https://openalex.org/W2367468405","https://openalex.org/W2952985052","https://openalex.org/W4300575715"],"abstract_inverted_index":{"Cohesive":[0],"subgraph":[1,16],"mining":[2,17],"on":[3,19,62,120,186],"attributed":[4,20,63],"graphs":[5,21,189],"is":[6],"a":[7,94,121],"fundamental":[8],"problem":[9],"in":[10,29],"graph":[11],"data":[12],"analysis.":[13],"Existing":[14],"cohesive":[15,50],"algorithms":[18],"do":[22],"not":[23],"consider":[24],"the":[25,30,37,43,129,191,197],"<i>fairness</i>":[26],"of":[27,183,196],"attributes":[28],"subgraph.":[31],"In":[32,52],"this":[33],"article,":[34],"we,":[35],"for":[36,138,163,177],"first":[38],"time,":[39],"introduce":[40],"fairness":[41],"into":[42],"widely-used":[44],"clique":[45,60,71,144],"model":[46],"to":[47,113],"mine":[48],"fairness-aware":[49,58],"subgraphs.":[51],"particular,":[53],"we":[54,83,131,152],"propose":[55,105],"three":[56],"novel":[57,95],"maximal":[59],"models":[61],"graphs,":[64],"called":[65,89,110],"weak":[66,80,140],"fair":[67,70,74,81,117,143,150],"clique,":[68,75],"strong":[69,116,142],"and":[72,141,166,174,194],"relative":[73,149],"respectively.":[76],"To":[77,126,146],"enumerate":[78,147],"all":[79,115,148],"cliques,":[82,151],"develop":[84,167],"an":[85,106,154],"efficient":[86,107,169],"backtracking":[87],"algorithm":[88,109],"<inline-formula><tex-math":[90,97,111,157,172,175],"notation=\"LaTeX\">$\\mathsf{WFCEnum}$</tex-math></inline-formula>":[91],"equipped":[92],"with":[93],"colorful":[96,156],"notation=\"LaTeX\">$k$</tex-math></inline-formula>":[98,158],"-core":[99,159],"based":[100,119,160],"pruning":[101,161],"technique.":[102,125],"We":[103],"also":[104,132],"enumeration":[108],"notation=\"LaTeX\">$\\mathsf{SFCEnum}$</tex-math></inline-formula>":[112],"find":[114],"cliques":[118],"new":[122],"attribute-alternatively-selection":[123],"search":[124,170],"further":[127],"improve":[128],"efficiency,":[130,192],"present":[133],"several":[134],"non-trivial":[135],"ordering":[136],"techniques":[137],"both":[139],"enumerations.":[145],"design":[153],"enhanced":[155],"technique":[162],"2D":[164],"attributes,":[165],"two":[168],"algorithms:":[171],"notation=\"LaTeX\">$\\mathsf{RFCRefineEnum}$</tex-math></inline-formula>":[173],"notation=\"LaTeX\">$\\mathsf{RFCAlterEnum}$</tex-math></inline-formula>":[176],"arbitrary":[178],"dimension":[179],"attributes.":[180],"The":[181],"results":[182],"extensive":[184],"experiments":[185],"four":[187],"real-world":[188],"demonstrate":[190],"scalability":[193],"effectiveness":[195],"proposed":[198],"algorithms.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3}],"updated_date":"2026-04-17T18:11:37.981687","created_date":"2025-10-10T00:00:00"}