{"id":"https://openalex.org/W2334899952","doi":"https://doi.org/10.1093/comnet/cnu045","title":"Adding cohesion constraints to models for modularity maximization in networks","display_name":"Adding cohesion constraints to models for modularity maximization in networks","publication_year":2014,"publication_date":"2014-12-29","ids":{"openalex":"https://openalex.org/W2334899952","doi":"https://doi.org/10.1093/comnet/cnu045","mag":"2334899952"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnu045","is_oa":true,"landing_page_url":"https://doi.org/10.1093/comnet/cnu045","pdf_url":"https://academic.oup.com/comnet/article-pdf/3/3/388/1084441/cnu045.pdf","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":true,"oa_status":"bronze","oa_url":"https://academic.oup.com/comnet/article-pdf/3/3/388/1084441/cnu045.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025519046","display_name":"Sonia Cafieri","orcid":"https://orcid.org/0000-0002-4578-8394"},"institutions":[{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I100296615","display_name":"\u00c9cole Nationale de l\u2019Aviation Civile","ror":"https://ror.org/022zdgq74","country_code":"FR","type":"education","lineage":["https://openalex.org/I100296615","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sonia Cafieri","raw_affiliation_strings":["ENAC, MAIAA, F-31055 Toulouse, France and Universit\u00e9 de Toulouse, IMT, F-31400 Toulouse, France"],"affiliations":[{"raw_affiliation_string":"ENAC, MAIAA, F-31055 Toulouse, France and Universit\u00e9 de Toulouse, IMT, F-31400 Toulouse, France","institution_ids":["https://openalex.org/I100296615","https://openalex.org/I17866349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030963458","display_name":"Alberto Costa","orcid":"https://orcid.org/0000-0002-1308-8510"},"institutions":[{"id":"https://openalex.org/I152815399","display_name":"Singapore University of Technology and Design","ror":"https://ror.org/05j6fvn87","country_code":"SG","type":"education","lineage":["https://openalex.org/I152815399"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Alberto Costa","raw_affiliation_strings":["Singapore University of Technology and Design, 138682, Singapore"],"affiliations":[{"raw_affiliation_string":"Singapore University of Technology and Design, 138682, Singapore","institution_ids":["https://openalex.org/I152815399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038480864","display_name":"Pierre Hansen","orcid":null},"institutions":[{"id":"https://openalex.org/I108192572","display_name":"HEC Montr\u00e9al","ror":"https://ror.org/05ww3wq27","country_code":"CA","type":"education","lineage":["https://openalex.org/I108192572"]},{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pierre Hansen","raw_affiliation_strings":["GERAD, HEC Montr\u00e9al, Canada H3T 2A7"],"affiliations":[{"raw_affiliation_string":"GERAD, HEC Montr\u00e9al, Canada H3T 2A7","institution_ids":["https://openalex.org/I108192572","https://openalex.org/I4210133247"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030963458"],"corresponding_institution_ids":["https://openalex.org/I152815399"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":1.1737,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80253091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"3","issue":"3","first_page":"388","last_page":"410"},"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":0.9889000058174133,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9868000149726868,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.6843602061271667},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.6747714877128601},{"id":"https://openalex.org/keywords/cohesion","display_name":"Cohesion (chemistry)","score":0.6297467947006226},{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.5631105303764343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5621823668479919},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45700231194496155},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.44486644864082336},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4217853248119354},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3536943793296814},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16163700819015503},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06290897727012634}],"concepts":[{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.6843602061271667},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.6747714877128601},{"id":"https://openalex.org/C104054115","wikidata":"https://www.wikidata.org/wiki/Q216828","display_name":"Cohesion (chemistry)","level":2,"score":0.6297467947006226},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.5631105303764343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5621823668479919},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45700231194496155},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.44486644864082336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4217853248119354},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3536943793296814},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16163700819015503},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06290897727012634},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","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":3,"locations":[{"id":"doi:10.1093/comnet/cnu045","is_oa":true,"landing_page_url":"https://doi.org/10.1093/comnet/cnu045","pdf_url":"https://academic.oup.com/comnet/article-pdf/3/3/388/1084441/cnu045.pdf","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.634.9825","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.634.9825","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal-enac.archives-ouvertes.fr/docs/00/99/16/94/PDF/Cafieri_GERAD2014.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00991694v1","is_oa":true,"landing_page_url":"https://enac.hal.science/hal-00991694","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Complex Networks, 2015, 3 (3), pp 388-410. ⟨10.1093/comnet/cnu045⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1093/comnet/cnu045","is_oa":true,"landing_page_url":"https://doi.org/10.1093/comnet/cnu045","pdf_url":"https://academic.oup.com/comnet/article-pdf/3/3/388/1084441/cnu045.pdf","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1273526789","display_name":null,"funder_award_id":"12-JS02-009-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3038135699","display_name":null,"funder_award_id":"009-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6851345361","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2334899952.pdf","grobid_xml":"https://content.openalex.org/works/W2334899952.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W5891020","https://openalex.org/W73486220","https://openalex.org/W1540051846","https://openalex.org/W1831254230","https://openalex.org/W1871641673","https://openalex.org/W1875112053","https://openalex.org/W1967140769","https://openalex.org/W1971421925","https://openalex.org/W1975308300","https://openalex.org/W1975606664","https://openalex.org/W1976702945","https://openalex.org/W1982322675","https://openalex.org/W1985625141","https://openalex.org/W2004531067","https://openalex.org/W2006177467","https://openalex.org/W2014259951","https://openalex.org/W2016621483","https://openalex.org/W2017987256","https://openalex.org/W2022615940","https://openalex.org/W2024514015","https://openalex.org/W2024996305","https://openalex.org/W2025543856","https://openalex.org/W2029373408","https://openalex.org/W2038920443","https://openalex.org/W2045387243","https://openalex.org/W2051741861","https://openalex.org/W2054152820","https://openalex.org/W2055747219","https://openalex.org/W2057504236","https://openalex.org/W2061099285","https://openalex.org/W2065555371","https://openalex.org/W2070326635","https://openalex.org/W2078528040","https://openalex.org/W2086805702","https://openalex.org/W2089023653","https://openalex.org/W2094234423","https://openalex.org/W2095012686","https://openalex.org/W2104293880","https://openalex.org/W2104615987","https://openalex.org/W2106278308","https://openalex.org/W2109726592","https://openalex.org/W2127048411","https://openalex.org/W2128366083","https://openalex.org/W2131681506","https://openalex.org/W2151936673","https://openalex.org/W2227911040","https://openalex.org/W2289882453","https://openalex.org/W2313362224","https://openalex.org/W3098765153","https://openalex.org/W3099768174","https://openalex.org/W3101413764","https://openalex.org/W3102641634","https://openalex.org/W3103615116","https://openalex.org/W3104653107","https://openalex.org/W3129907499","https://openalex.org/W4238452917"],"related_works":["https://openalex.org/W4230687177","https://openalex.org/W1968829728","https://openalex.org/W2349859869","https://openalex.org/W2051365847","https://openalex.org/W2367249529","https://openalex.org/W3120118008","https://openalex.org/W4214765864","https://openalex.org/W1943342825","https://openalex.org/W2042226922","https://openalex.org/W2217121926"],"abstract_inverted_index":{"Finding":[0],"communities":[1,87,227,242],"in":[2,15,88,111],"complex":[3],"networks":[4],"is":[5,34,202],"a":[6,89,122,152,157,250],"topic":[7],"of":[8,32,57,95,175,212,218,241,267,271,285,289],"much":[9],"current":[10],"research":[11],"and":[12,143,183,193,243,257],"has":[13,51],"applications":[14],"many":[16],"domains.":[17],"On":[18,36],"the":[19,29,37,58,64,96,126,173,194,213,238,254,264,283,286,290],"one":[20,56,84,150],"hand,":[21,39],"criteria":[22],"for":[23,224],"doing":[24],"so":[25],"have":[26,47],"been":[27,48,53],"proposed,":[28],"most":[30],"studied":[31],"which":[33,91,134,167,225],"modularity.":[35,268],"other":[38],"properties":[40],"to":[41,116,125,156,188,262,275,279],"be":[42,189,280],"satisfied":[43,82],"by":[44,68,83,104,120,204],"each":[45],"community":[46],"suggested.":[49],"It":[50,100],"recently":[52],"observed":[54],"that":[55,253],"best":[59,97],"known":[60,98,251],"such":[61],"properties,":[62],"i.e.":[63],"weak":[65,127,142,200],"condition,":[66],"proposed":[67,103],"Radicchi":[69],"et":[70,106],"al.":[71,107],"(2004,":[72],"Proc.":[73],"Natl.":[74],"Acad.":[75],"Sci.":[76],"USA,":[77],"101,":[78],"2658)":[79],"was":[80,101],"not":[81,207,229],"or":[85],"more":[86],"partition":[90],"maximizes":[92],"(approximately)":[93],"some":[94,205,226],"criteria.":[99],"therefore":[102],"Wang":[105],"(2009,":[108],"Lect.":[109],"Notes":[110],"Oper.":[112],"Res.,":[113],"11,":[114],"142)":[115],"merge":[117],"both":[118],"approaches":[119],"maximizing":[121,210],"criterion":[123],"subject":[124,274],"condition.":[128],"We":[129,146,171,246],"consider":[130],"five":[131],"community-defining":[132],"conditions,":[133,149],"we":[135,168],"call":[136],"cohesion":[137,148,176,185,276],"conditions":[138,177,186,259],"(strong,":[139],"semi-strong,":[140],"almost-strong,":[141],"extra-weak":[144,195],"conditions).":[145],"add":[147],"at":[151],"time,":[153],"as":[154],"constraints":[155,277],"modularity":[158,179,209,233,272],"maximization":[159,273],"problem,":[160],"thus":[161],"obtaining":[162],"new":[163],"mathematical":[164],"optimization":[165],"models,":[166],"solve":[169],"exactly.":[170],"study":[172],"impact":[174],"on":[178,221,249],"maximization.":[180],"Strong,":[181],"semi-strong":[182,256],"almost-strong":[184,258],"appear":[187],"generally":[190],"too":[191,197],"restrictive":[192],"condition":[196,201,220],"lax.":[198],"The":[199,269],"verified":[203],"but":[206,235],"all":[208],"partitions":[211,223],"considered":[214,291],"real-world":[215],"networks.":[216,292],"Imposition":[217],"this":[219],"those":[222],"do":[228],"verify":[230],"it":[231],"reduces":[232],"moderately":[234],"sometimes":[236],"changes":[237],"optimal":[239],"number":[240],"their":[244],"composition.":[245],"also":[247],"show,":[248],"example,":[252],"strong,":[255],"allow":[260],"us":[261],"overcome":[263],"resolution":[265],"limit":[266],"behaviour":[270],"appears":[278],"coherent":[281],"with":[282],"detectability":[284],"modular":[287],"structure":[288]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}