{"id":"https://openalex.org/W2024996305","doi":"https://doi.org/10.1007/s10479-012-1286-z","title":"Reformulation of a model for hierarchical divisive graph modularity maximization","display_name":"Reformulation of a model for hierarchical divisive graph modularity maximization","publication_year":2012,"publication_date":"2012-12-28","ids":{"openalex":"https://openalex.org/W2024996305","doi":"https://doi.org/10.1007/s10479-012-1286-z","mag":"2024996305"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-012-1286-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10479-012-1286-z","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","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/A5025519046","display_name":"Sonia Cafieri","orcid":"https://orcid.org/0000-0002-4578-8394"},"institutions":[{"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"]},{"id":"https://openalex.org/I4210102957","display_name":"D\u00e9partement math\u00e9matiques, informatique, sciences de la donn\u00e9e et technologies du num\u00e9rique","ror":"https://ror.org/011emb038","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210088668","https://openalex.org/I4210102957"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sonia Cafieri","raw_affiliation_strings":["Laboratoire MAIAA, \u00c9cole Nationale de l\u2019Aviation Civile, 7 Ave. E. Belin, 31055, Toulouse, France","ENAC - Laboratoire de Math\u00e9matiques Appliqu\u00e9es, Informatique et Automatique pour l'A\u00e9rien"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire MAIAA, \u00c9cole Nationale de l\u2019Aviation Civile, 7 Ave. E. Belin, 31055, Toulouse, France","institution_ids":["https://openalex.org/I100296615"]},{"raw_affiliation_string":"ENAC - Laboratoire de Math\u00e9matiques Appliqu\u00e9es, Informatique et Automatique pour l'A\u00e9rien","institution_ids":["https://openalex.org/I4210102957","https://openalex.org/I4210155549"]}]},{"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/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Alberto Costa","raw_affiliation_strings":["LIX, \u00c9cole Polytechnique, 91128, Palaiseau, France","Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIX, \u00c9cole Polytechnique, 91128, Palaiseau, France","institution_ids":["https://openalex.org/I4210139461"]},{"raw_affiliation_string":"Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau]","institution_ids":["https://openalex.org/I4210139461"]}]},{"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/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["CA","FR"],"is_corresponding":false,"raw_author_name":"Pierre Hansen","raw_affiliation_strings":["GERAD, HEC, 3000 Chemin de la C\u00f4te-Sainte-Catherine, Montr\u00e9al, Canada, H3T 2A7","LIX, \u00c9cole Polytechnique, 91128, Palaiseau, France","Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau]","HEC Montr\u00e9al"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"GERAD, HEC, 3000 Chemin de la C\u00f4te-Sainte-Catherine, Montr\u00e9al, Canada, H3T 2A7","institution_ids":["https://openalex.org/I108192572"]},{"raw_affiliation_string":"LIX, \u00c9cole Polytechnique, 91128, Palaiseau, France","institution_ids":["https://openalex.org/I4210139461"]},{"raw_affiliation_string":"Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau]","institution_ids":["https://openalex.org/I4210139461"]},{"raw_affiliation_string":"HEC Montr\u00e9al","institution_ids":["https://openalex.org/I108192572"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030963458"],"corresponding_institution_ids":["https://openalex.org/I4210139461"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.1859,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.87304575,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"222","issue":"1","first_page":"213","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9961000084877014,"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":0.9961000084877014,"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":0.9509000182151794,"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/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9491999745368958,"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/heuristics","display_name":"Heuristics","score":0.733485758304596},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5639622211456299},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5176761150360107},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5114620923995972},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5013682842254639},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46754851937294006},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4499262571334839},{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.43337881565093994},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.41678088903427124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3788304328918457},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.349674791097641},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26148247718811035}],"concepts":[{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.733485758304596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5639622211456299},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5176761150360107},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5114620923995972},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5013682842254639},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46754851937294006},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4499262571334839},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.43337881565093994},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.41678088903427124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3788304328918457},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.349674791097641},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26148247718811035},{"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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10479-012-1286-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10479-012-1286-z","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00979234v1","is_oa":false,"landing_page_url":"https://enac.hal.science/hal-00979234","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Annals of Operations Research, 2012, pp 1-14. &#x27E8;10.1007/s10479-012-1286-z&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:annopr:v:222:y:2014:i:1:p:213-226:10.1007/s10479-012-1286-z","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10479-012-1286-z","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321747","display_name":"Fonds Qu\u00e9b\u00e9cois de la Recherche sur la Nature et les Technologies","ror":"https://ror.org/00b9f9778"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1875112053","https://openalex.org/W1967140769","https://openalex.org/W1971421925","https://openalex.org/W1976702945","https://openalex.org/W1992162584","https://openalex.org/W1995907191","https://openalex.org/W2006177467","https://openalex.org/W2015953751","https://openalex.org/W2016621483","https://openalex.org/W2017987256","https://openalex.org/W2025543856","https://openalex.org/W2035661922","https://openalex.org/W2038920443","https://openalex.org/W2045387243","https://openalex.org/W2047940964","https://openalex.org/W2051741861","https://openalex.org/W2055747219","https://openalex.org/W2057504236","https://openalex.org/W2061099285","https://openalex.org/W2072884723","https://openalex.org/W2094234423","https://openalex.org/W2095293504","https://openalex.org/W2102931907","https://openalex.org/W2104293880","https://openalex.org/W2104615987","https://openalex.org/W2106278308","https://openalex.org/W2109726592","https://openalex.org/W2112090702","https://openalex.org/W2127048411","https://openalex.org/W2128366083","https://openalex.org/W2142097077","https://openalex.org/W2149844425","https://openalex.org/W2151936673","https://openalex.org/W2163815837","https://openalex.org/W2164928285","https://openalex.org/W2171960770","https://openalex.org/W3098765153","https://openalex.org/W3101413764","https://openalex.org/W3102641634","https://openalex.org/W4238452917","https://openalex.org/W6657150744"],"related_works":["https://openalex.org/W2280422768","https://openalex.org/W3143197806","https://openalex.org/W4230687177","https://openalex.org/W4252555497","https://openalex.org/W1968829728","https://openalex.org/W2349859869","https://openalex.org/W3121175838","https://openalex.org/W3016293053","https://openalex.org/W2401723157","https://openalex.org/W2051365847"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
