{"id":"https://openalex.org/W3133655341","doi":"https://doi.org/10.1093/comnet/cnaa047","title":"Detecting the number of clusters in a network","display_name":"Detecting the number of clusters in a network","publication_year":2020,"publication_date":"2020-12-01","ids":{"openalex":"https://openalex.org/W3133655341","doi":"https://doi.org/10.1093/comnet/cnaa047","mag":"3133655341"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnaa047","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnaa047","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","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/A5069157357","display_name":"Gabriel Budel","orcid":"https://orcid.org/0000-0003-0622-6492"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Gabriel Budel","raw_affiliation_strings":["Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001877366","display_name":"Piet Van Mieghem","orcid":"https://orcid.org/0000-0002-3786-7922"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Piet Van Mieghem","raw_affiliation_strings":["Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069157357"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.6638,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.68804097,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"8","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9796000123023987,"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/T13283","display_name":"Mental Health Research Topics","score":0.9726999998092651,"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/backtracking","display_name":"Backtracking","score":0.8397971391677856},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6381618976593018},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5948433876037598},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5672028064727783},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.5408064126968384},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5311958193778992},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5227687358856201},{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.4931921362876892},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.4909651577472687},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4225695729255676},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39960020780563354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3736805319786072},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.34435945749282837},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3270595371723175},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1604030430316925},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09610581398010254},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06763359904289246}],"concepts":[{"id":"https://openalex.org/C156884757","wikidata":"https://www.wikidata.org/wiki/Q798554","display_name":"Backtracking","level":2,"score":0.8397971391677856},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6381618976593018},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5948433876037598},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5672028064727783},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.5408064126968384},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5311958193778992},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5227687358856201},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.4931921362876892},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.4909651577472687},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4225695729255676},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39960020780563354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3736805319786072},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.34435945749282837},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3270595371723175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1604030430316925},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09610581398010254},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06763359904289246},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/comnet/cnaa047","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnaa047","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W141418607","https://openalex.org/W658559791","https://openalex.org/W1506690472","https://openalex.org/W1508988789","https://openalex.org/W1523808012","https://openalex.org/W1595344052","https://openalex.org/W1871641673","https://openalex.org/W1872749931","https://openalex.org/W2013737143","https://openalex.org/W2015953751","https://openalex.org/W2023655578","https://openalex.org/W2023708440","https://openalex.org/W2024514015","https://openalex.org/W2042554123","https://openalex.org/W2049294562","https://openalex.org/W2049433041","https://openalex.org/W2089004939","https://openalex.org/W2093690536","https://openalex.org/W2095293504","https://openalex.org/W2108614537","https://openalex.org/W2116819994","https://openalex.org/W2127048411","https://openalex.org/W2128366083","https://openalex.org/W2131681506","https://openalex.org/W2142370107","https://openalex.org/W2151936673","https://openalex.org/W2152361742","https://openalex.org/W2155461593","https://openalex.org/W2196782699","https://openalex.org/W2375070860","https://openalex.org/W2531871281","https://openalex.org/W2550720082","https://openalex.org/W2622042591","https://openalex.org/W3099768174","https://openalex.org/W3101413764","https://openalex.org/W3102641634","https://openalex.org/W3103588369","https://openalex.org/W3106359669","https://openalex.org/W4213281018","https://openalex.org/W4251636534","https://openalex.org/W6630448470","https://openalex.org/W6631205662","https://openalex.org/W6683180375"],"related_works":["https://openalex.org/W2760348722","https://openalex.org/W2783885583","https://openalex.org/W2120095724","https://openalex.org/W2368326437","https://openalex.org/W1631221657","https://openalex.org/W2357479099","https://openalex.org/W2364309619","https://openalex.org/W1525406239","https://openalex.org/W2371864976","https://openalex.org/W2391415040"],"abstract_inverted_index":{"Abstract":[0],"Many":[1],"clustering":[2,145],"algorithms":[3],"for":[4,11,105,135,141],"complex":[5],"networks":[6],"depend":[7],"on":[8,76,85],"the":[9,12,35,38,48,57,60,66,69,77,83,92,96,102,106,114,123,130,147,163,168],"choice":[10],"number":[13,27,49,61,97,132,164],"of":[14,28,37,47,50,59,62,68,79,98,122,133,159,162,165,170,174],"clusters":[15,51,63,99,115,134],"and":[16,81],"it":[17],"is":[18,155],"often":[19],"unclear":[20],"how":[21],"to":[22,43],"make":[23],"this":[24],"choice.":[25],"The":[26,120],"eigenvalues":[29],"located":[30],"outside":[31],"a":[32,53,144,156,171,175],"circle":[33],"in":[34,52,108],"spectrum":[36,67],"non-backtracking":[39,70,93,124,148],"matrix":[40,71],"was":[41],"conjectured":[42],"be":[44],"an":[45,160],"estimator":[46,161],"graph.":[54],"We":[55,89],"compare":[56],"estimate":[58],"obtained":[64],"from":[65],"with":[72],"three":[73],"estimators":[74],"based":[75],"concept":[78,173],"modularity":[80],"evaluate":[82],"methods":[84,104],"several":[86],"benchmark":[87,137],"graphs.":[88],"find":[90],"that":[91],"method":[94,125,149],"detects":[95,150],"better":[100],"than":[101],"modularity-based":[103],"graphs":[107,138,142],"our":[109],"simulation":[110],"study,":[111],"especially":[112],"when":[113],"have":[116],"slightly":[117],"different":[118],"sizes.":[119],"estimates":[121],"are":[126],"narrowly":[127],"distributed":[128],"around":[129],"true":[131],"all":[136],"considered.":[139],"Additionally,":[140],"without":[143],"structure,":[146],"exactly":[151],"one":[152],"cluster,":[153],"which":[154],"convenient":[157],"property":[158],"clusters.":[166],"However,":[167],"lack":[169],"well-defined":[172],"cluster":[176],"prevents":[177],"sharp":[178],"conclusions.":[179]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
