{"id":"https://openalex.org/W2796036701","doi":"https://doi.org/10.1137/18m1231304","title":"Relating Modularity Maximization and Stochastic Block Models in Multilayer Networks","display_name":"Relating Modularity Maximization and Stochastic Block Models in Multilayer Networks","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2796036701","doi":"https://doi.org/10.1137/18m1231304","mag":"2796036701"},"language":"en","primary_location":{"id":"doi:10.1137/18m1231304","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1231304","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/18m1231304","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009117991","display_name":"A. Roxana Pamfil","orcid":"https://orcid.org/0000-0002-5019-3731"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Roxana Pamfil","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053246739","display_name":"Sam Howison","orcid":"https://orcid.org/0000-0001-7938-370X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sam D. Howison","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034372799","display_name":"Renaud Lambiotte","orcid":"https://orcid.org/0000-0002-0583-4595"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Renaud Lambiotte","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058684689","display_name":"Mason A. Porter","orcid":"https://orcid.org/0000-0002-5166-0717"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mason A. Porter","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5009117991"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1517,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77476086,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"1","issue":"4","first_page":"667","last_page":"698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9889000058174133,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9889000058174133,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9657999873161316,"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/T11195","display_name":"Simulation Techniques and Applications","score":0.9652000069618225,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.7878886461257935},{"id":"https://openalex.org/keywords/stochastic-block-model","display_name":"Stochastic block model","score":0.7091373801231384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7041343450546265},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5671107769012451},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5349612832069397},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5009310245513916},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.47506067156791687},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4352143406867981},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3287726640701294},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29442891478538513},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21644437313079834},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.14284920692443848}],"concepts":[{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.7878886461257935},{"id":"https://openalex.org/C2779982251","wikidata":"https://www.wikidata.org/wiki/Q25053762","display_name":"Stochastic block model","level":3,"score":0.7091373801231384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7041343450546265},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5671107769012451},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5349612832069397},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5009310245513916},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.47506067156791687},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4352143406867981},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3287726640701294},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29442891478538513},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21644437313079834},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.14284920692443848},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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":5,"locations":[{"id":"doi:10.1137/18m1231304","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1231304","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1804.01964","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.01964","pdf_url":"https://arxiv.org/pdf/1804.01964","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2796036701","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.01964.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:ora.ox.ac.uk:uuid:7f7ac3d4-fda6-49e8-9c01-124407200e48","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:7f7ac3d4-fda6-49e8-9c01-124407200e48","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"},{"id":"doi:10.48550/arxiv.1804.01964","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.01964","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1137/18m1231304","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1231304","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G667190850","display_name":"EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling","funder_award_id":"EP/L015803/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W745973578","https://openalex.org/W1470088430","https://openalex.org/W1871641673","https://openalex.org/W1930572491","https://openalex.org/W1931149371","https://openalex.org/W1978825280","https://openalex.org/W1983099884","https://openalex.org/W1997912386","https://openalex.org/W2004531067","https://openalex.org/W2008209917","https://openalex.org/W2015953751","https://openalex.org/W2021969955","https://openalex.org/W2024128809","https://openalex.org/W2025543856","https://openalex.org/W2038224551","https://openalex.org/W2043997271","https://openalex.org/W2044988896","https://openalex.org/W2050766178","https://openalex.org/W2054323527","https://openalex.org/W2061099285","https://openalex.org/W2061901927","https://openalex.org/W2070746915","https://openalex.org/W2074617510","https://openalex.org/W2095293504","https://openalex.org/W2098005762","https://openalex.org/W2109726592","https://openalex.org/W2119998616","https://openalex.org/W2125598538","https://openalex.org/W2127048411","https://openalex.org/W2128366083","https://openalex.org/W2131681506","https://openalex.org/W2134662941","https://openalex.org/W2153649056","https://openalex.org/W2157547297","https://openalex.org/W2164998314","https://openalex.org/W2252566672","https://openalex.org/W2265944008","https://openalex.org/W2342114889","https://openalex.org/W2489125130","https://openalex.org/W2513567506","https://openalex.org/W2550720082","https://openalex.org/W2575287576","https://openalex.org/W2583143836","https://openalex.org/W2622042591","https://openalex.org/W2626936883","https://openalex.org/W2742510161","https://openalex.org/W2743619017","https://openalex.org/W2767544505","https://openalex.org/W2901605853","https://openalex.org/W2951271819","https://openalex.org/W2962929315","https://openalex.org/W2963041679","https://openalex.org/W2963066686","https://openalex.org/W2963104673","https://openalex.org/W2963499979","https://openalex.org/W2963728441","https://openalex.org/W2963831122","https://openalex.org/W2963847248","https://openalex.org/W2964035435","https://openalex.org/W3037819556","https://openalex.org/W3037826211","https://openalex.org/W3133780092"],"related_works":["https://openalex.org/W2074617510","https://openalex.org/W2131681506","https://openalex.org/W2095293504","https://openalex.org/W2748287123","https://openalex.org/W2963104673","https://openalex.org/W2416738288","https://openalex.org/W2127048411","https://openalex.org/W2566534050","https://openalex.org/W3038358646","https://openalex.org/W2333350679","https://openalex.org/W2504964546","https://openalex.org/W3111634167","https://openalex.org/W2916761058","https://openalex.org/W3015546966","https://openalex.org/W2291701016","https://openalex.org/W3105734402","https://openalex.org/W3102446989","https://openalex.org/W3037819556","https://openalex.org/W2102907934","https://openalex.org/W1194254716"],"abstract_inverted_index":{"Characterizing":[0],"large-scale":[1],"organization":[2],"in":[3,15,32,91,137,148,154,196,206],"networks,":[4,7],"including":[5,128],"multilayer":[6,92,126,177],"is":[8,19,29,97],"one":[9],"of":[10,26,35,48,51,107,119,125,164,176,184,187,216],"the":[11,52,104,139,155,165,182,214],"most":[12,53],"prominent":[13],"topics":[14],"network":[16],"science":[17],"and":[18,67,131,211,222],"important":[20],"for":[21,56,122],"many":[22],"applications.":[23],"One":[24],"type":[25],"mesoscale":[27],"feature":[28],"community":[30,57,108],"structure,":[31],"which":[33,138,149,180],"sets":[34,47,186],"nodes":[36],"are":[37,59,142],"densely":[38],"connected":[39,43],"internally":[40],"but":[41],"sparsely":[42],"to":[44,60,68,102,194,201],"other":[45],"dense":[46],"nodes.":[49],"Two":[50],"popular":[54],"approaches":[55],"detection":[58],"maximize":[61],"an":[62],"objective":[63],"function":[64],"called":[65],"\u201cmodularity\u201d":[66],"perform":[69,202],"statistical":[70],"inference":[71],"using":[72],"stochastic":[73,113],"block":[74,114],"models.":[75,115],"Inspired":[76],"by":[77],"Newman's":[78],"work":[79],"on":[80,219],"monolayer":[81],"networks":[82,93],"[Phys.":[83],"Rev.":[84],"E,":[85],"94":[86],"(2016),":[87],"052315],":[88],"we":[89,212],"show":[90,199],"that":[94,190],"maximizing":[95,103],"modularity":[96,166],"equivalent,":[98],"under":[99,110],"certain":[100],"conditions,":[101],"posterior":[105],"probability":[106],"assignments":[109],"suitably":[111],"chosen":[112],"We":[116,134,198],"derive":[117],"versions":[118],"this":[120,158,203],"equivalence":[121],"various":[123],"types":[124],"structures,":[127],"temporal,":[129],"multiplex,":[130],"multilevel":[132],"networks.":[133,224],"consider":[135],"cases":[136],"key":[140],"parameters":[141,189],"constant,":[143],"as":[144,146],"well":[145],"ones":[147],"they":[150],"vary":[151],"across":[152],"layers;":[153],"latter":[156],"case,":[157],"yields":[159],"a":[160,173,207],"novel,":[161],"layer-weighted":[162],"version":[163],"function.":[167],"Our":[168],"results":[169],"also":[170],"help":[171],"address":[172],"longstanding":[174],"difficulty":[175],"modularity-maximization":[178],"algorithms,":[179],"require":[181],"specification":[183],"two":[185],"tuning":[188],"have":[191],"been":[192],"difficult":[193],"choose":[195],"practice.":[197],"how":[200],"parameter":[204],"selection":[205],"statistically":[208],"grounded":[209],"way,":[210],"demonstrate":[213],"effectiveness":[215],"our":[217],"approach":[218],"both":[220],"synthetic":[221],"empirical":[223]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
