{"id":"https://openalex.org/W7151585503","doi":"https://doi.org/10.1145/3806834","title":"Maximal Balanced Quasi-Clique Enumeration in Signed Graphs","display_name":"Maximal Balanced Quasi-Clique Enumeration in Signed Graphs","publication_year":2026,"publication_date":"2026-04-07","ids":{"openalex":"https://openalex.org/W7151585503","doi":"https://doi.org/10.1145/3806834"},"language":"en","primary_location":{"id":"doi:10.1145/3806834","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3806834","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Knowledge Discovery from Data","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1145/3806834","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084474796","display_name":"Jie Gao","orcid":"https://orcid.org/0000-0002-3542-5389"},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jie Gao","raw_affiliation_strings":["Department of Computer Science, University of Exeter, Exeter, United Kingdom of Great Britain and Northern Ireland"],"raw_orcid":"https://orcid.org/0000-0002-3542-5389","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Exeter, Exeter, United Kingdom of Great Britain and Northern Ireland","institution_ids":["https://openalex.org/I23923803"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133089058","display_name":"Jia Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jia Hu","raw_affiliation_strings":["Department of Computer Science, University of Exeter, Exeter, United Kingdom of Great Britain and Northern Ireland"],"raw_orcid":"https://orcid.org/0000-0001-5406-8420","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Exeter, Exeter, United Kingdom of Great Britain and Northern Ireland","institution_ids":["https://openalex.org/I23923803"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133067595","display_name":"Fei Hao","orcid":null},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fei Hao","raw_affiliation_strings":["School of Artificial Intelligence and Computer Science, Shaanxi Normal University, Xi\u2019an, China"],"raw_orcid":"https://orcid.org/0000-0001-5288-5523","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Computer Science, Shaanxi Normal University, Xi\u2019an, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133103594","display_name":"Geyong Min","orcid":null},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Geyong Min","raw_affiliation_strings":["Department of Computer Science, University of Exeter, Exeter, United Kingdom of Great Britain and Northern Ireland"],"raw_orcid":"https://orcid.org/0000-0003-1395-7314","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Exeter, Exeter, United Kingdom of Great Britain and Northern Ireland","institution_ids":["https://openalex.org/I23923803"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5133107792","display_name":"Lei Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Liu","raw_affiliation_strings":["School of Software, Shandong University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-4646-2054","affiliations":[{"raw_affiliation_string":"School of Software, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.39159528,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"5","first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.4090000092983246,"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":0.4090000092983246,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.37610000371932983,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.06889999657869339,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.840399980545044},{"id":"https://openalex.org/keywords/signed-graph","display_name":"Signed graph","score":0.6959999799728394},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6136999726295471},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4323999881744385},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.40130001306533813}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.840399980545044},{"id":"https://openalex.org/C2779773260","wikidata":"https://www.wikidata.org/wiki/Q11246292","display_name":"Signed graph","level":3,"score":0.6959999799728394},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6136999726295471},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5414000153541565},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48570001125335693},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4397999942302704},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43050000071525574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40459999442100525},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3596000075340271},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.26100000739097595}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3806834","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3806834","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Knowledge Discovery from Data","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3806834","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3806834","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Knowledge Discovery from Data","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1873015260","display_name":null,"funder_award_id":"EP/Y036786/1","funder_id":"https://openalex.org/F4320314731","funder_display_name":"UK Research and Innovation"}],"funders":[{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W192462150","https://openalex.org/W2001966531","https://openalex.org/W2046643693","https://openalex.org/W2083392533","https://openalex.org/W2106650313","https://openalex.org/W2120904649","https://openalex.org/W2156894402","https://openalex.org/W2165997484","https://openalex.org/W2770987319","https://openalex.org/W2962788915","https://openalex.org/W2963716229","https://openalex.org/W2984323893","https://openalex.org/W2985096261","https://openalex.org/W3012937529","https://openalex.org/W3127171762","https://openalex.org/W3133302368","https://openalex.org/W3160800264","https://openalex.org/W3215246527","https://openalex.org/W4289533973","https://openalex.org/W4289866503","https://openalex.org/W4313065576","https://openalex.org/W4368232805","https://openalex.org/W4380433164","https://openalex.org/W4388620452","https://openalex.org/W4400297520","https://openalex.org/W4401352856","https://openalex.org/W4408519533","https://openalex.org/W4409149738"],"related_works":[],"abstract_inverted_index":{"Quasi-clique":[0],"is":[1,134],"one":[2],"of":[3,83,102,161],"the":[4,68,81,89,100,156],"most":[5],"fundamental":[6],"models":[7],"for":[8,24,60,94],"characterizing":[9],"cohesive":[10],"subgraphs":[11],"in":[12,105,129],"network":[13],"analysis.":[14],"However,":[15],"existing":[16],"quasi-clique":[17,57],"definitions":[18],"and":[19,38,43,110,146,159,165],"identification":[20],"algorithms":[21],"are":[22,31],"designed":[23],"unsigned":[25],"graphs,":[26],"while":[27],"many":[28],"real-world":[29,153],"networks":[30],"modeled":[32],"as":[33],"signed":[34,61,95,108,131],"graphs":[35],"with":[36,88,137],"positive":[37],"negative":[39],"edges":[40],"representing":[41],"cooperative":[42],"adversarial":[44],"interactions":[45],"between":[46],"entities.":[47],"Therefore,":[48],"it":[49],"remains":[50],"an":[51],"open":[52],"problem":[53,101],"to":[54,124,141],"define":[55],"a":[56,106,120,130],"model":[58,164],"tailored":[59],"graphs.":[62,96],"Motivated":[63],"by":[64],"this,":[65],"we":[66,98,118],"propose":[67],"maximal":[69],"balanced":[70],"\\(":[71],"(\\gamma_{1},\\gamma_{2})":[72],"\\)":[73],"-quasi-clique":[74],"(MBQC)":[75],"model,":[76],"which":[77,133],"not":[78],"only":[79],"preserves":[80],"essence":[82],"quasi-completeness":[84],"but":[85],"also":[86],"aligns":[87],"foremost":[90],"structural":[91],"balance":[92],"theory":[93],"Specifically,":[97],"formulate":[99],"MBQCs":[103,128],"enumeration":[104,148],"given":[107],"graph":[109],"prove":[111],"its":[112],"NP-hardness.":[113],"To":[114],"address":[115],"this":[116],"problem,":[117],"devise":[119],"novel":[121],"branch-and-bound":[122],"algorithm":[123],"efficiently":[125],"enumerate":[126],"all":[127],"graph,":[132],"further":[135],"optimized":[136],"several":[138],"carefully-crafted":[139],"techniques":[140],"prune":[142],"unpromising":[143],"search":[144],"spaces":[145],"enhance":[147],"efficiency.":[149],"Extensive":[150],"experiments":[151],"on":[152],"datasets":[154],"demonstrate":[155],"efficiency,":[157],"scalability,":[158],"effectiveness":[160],"our":[162],"MBQC":[163],"algorithms.":[166]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-04-08T00:00:00"}
