{"id":"https://openalex.org/W2140783379","doi":"https://doi.org/10.1093/comnet/cnu042","title":"Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs","display_name":"Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs","publication_year":2014,"publication_date":"2014-10-02","ids":{"openalex":"https://openalex.org/W2140783379","doi":"https://doi.org/10.1093/comnet/cnu042","mag":"2140783379"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnu042","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnu042","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1306.5794","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001647657","display_name":"Richard K. Darst","orcid":"https://orcid.org/0000-0002-0402-7994"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]},{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI","US"],"is_corresponding":true,"raw_author_name":"Richard K. Darst","raw_affiliation_strings":["Department of Chemistry, Columbia University, 3000 Broadway, New York, NY 10027, USA and Department of Biomedical Engineering and Computational Science, P.O. Box 12200, FI-00076 Aalto, Finlandrichard.darst@aalto.fi","Department of Chemistry, Columbia University, 3000 Broadway, New York, NY 10027, USA and Department of Biomedical Engineering and Computational Science, P.O. Box 12200, FI-00076 Aalto, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Columbia University, 3000 Broadway, New York, NY 10027, USA and Department of Biomedical Engineering and Computational Science, P.O. Box 12200, FI-00076 Aalto, Finlandrichard.darst@aalto.fi","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Department of Chemistry, Columbia University, 3000 Broadway, New York, NY 10027, USA and Department of Biomedical Engineering and Computational Science, P.O. Box 12200, FI-00076 Aalto, Finland","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014624803","display_name":"David R. Reichman","orcid":"https://orcid.org/0000-0002-5265-5637"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David R. Reichman","raw_affiliation_strings":["Department of Chemistry, Columbia University, 3000 Broadway, New York, NY 10027, USA","Department of Chemistry, Columbia University, 3000 Broadway, New York, NY\u00a010027, USA"],"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Columbia University, 3000 Broadway, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Department of Chemistry, Columbia University, 3000 Broadway, New York, NY\u00a010027, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034453648","display_name":"Peter Ronhovde","orcid":null},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Ronhovde","raw_affiliation_strings":["Department of Physics, Washington University in St. Louis, Campus Box 1105, 1 Brookings Drive, St Louis, MO 63130, USA","#N#Department of Physics, Washington University in St. Louis, Campus Box 1105, 1 Brookings Drive, St. Louis, MO 63130, USA"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Washington University in St. Louis, Campus Box 1105, 1 Brookings Drive, St Louis, MO 63130, USA","institution_ids":["https://openalex.org/I204465549"]},{"raw_affiliation_string":"#N#Department of Physics, Washington University in St. Louis, Campus Box 1105, 1 Brookings Drive, St. Louis, MO 63130, USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083751736","display_name":"Zohar Nussinov","orcid":"https://orcid.org/0000-0001-7947-7829"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zohar Nussinov","raw_affiliation_strings":["#N#Department of Physics, Washington University in St. Louis, Campus Box 1105, 1 Brookings Drive, St. Louis, MO 63130, USA"],"affiliations":[{"raw_affiliation_string":"#N#Department of Physics, Washington University in St. Louis, Campus Box 1105, 1 Brookings Drive, St. Louis, MO 63130, USA","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001647657"],"corresponding_institution_ids":["https://openalex.org/I78577930","https://openalex.org/I9927081"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15001459,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":"3","first_page":"333","last_page":"360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9883000254631042,"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/T11896","display_name":"Opportunistic and Delay-Tolerant Networks","score":0.9035000205039978,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/stochastic-block-model","display_name":"Stochastic block model","score":0.7422265410423279},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7011930346488953},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5870826244354248},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5113527178764343},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5106835961341858},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.5061323046684265},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5013654232025146},{"id":"https://openalex.org/keywords/community-structure","display_name":"Community structure","score":0.49823951721191406},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.488662987947464},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.45061835646629333},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4365408718585968},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.41355788707733154},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3822128176689148},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3623747229576111},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3607847988605499},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3218027353286743},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.29014599323272705},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16081738471984863}],"concepts":[{"id":"https://openalex.org/C2779982251","wikidata":"https://www.wikidata.org/wiki/Q25053762","display_name":"Stochastic block model","level":3,"score":0.7422265410423279},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7011930346488953},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5870826244354248},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5113527178764343},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5106835961341858},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.5061323046684265},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5013654232025146},{"id":"https://openalex.org/C133079900","wikidata":"https://www.wikidata.org/wiki/Q5155065","display_name":"Community structure","level":2,"score":0.49823951721191406},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.488662987947464},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.45061835646629333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4365408718585968},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.41355788707733154},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3822128176689148},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3623747229576111},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3607847988605499},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3218027353286743},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29014599323272705},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16081738471984863},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1093/comnet/cnu042","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnu042","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"},{"id":"pmh:oai:arXiv.org:1306.5794","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1306.5794","pdf_url":"https://arxiv.org/pdf/1306.5794","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:2140783379","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1306.5794.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":"doi:10.48550/arxiv.1306.5794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1306.5794","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":"pmh:oai:arXiv.org:1306.5794","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1306.5794","pdf_url":"https://arxiv.org/pdf/1306.5794","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2140783379.pdf","grobid_xml":"https://content.openalex.org/works/W2140783379.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1518885151","https://openalex.org/W1605711022","https://openalex.org/W1871641673","https://openalex.org/W1971729008","https://openalex.org/W1972542451","https://openalex.org/W1975606664","https://openalex.org/W1991408655","https://openalex.org/W1992107140","https://openalex.org/W2012600438","https://openalex.org/W2012662151","https://openalex.org/W2014259951","https://openalex.org/W2017620474","https://openalex.org/W2023655578","https://openalex.org/W2025543856","https://openalex.org/W2033947830","https://openalex.org/W2034561322","https://openalex.org/W2036882345","https://openalex.org/W2038635718","https://openalex.org/W2038920443","https://openalex.org/W2041713562","https://openalex.org/W2057552436","https://openalex.org/W2061849527","https://openalex.org/W2087544816","https://openalex.org/W2091469954","https://openalex.org/W2095189226","https://openalex.org/W2095293504","https://openalex.org/W2102907934","https://openalex.org/W2108880587","https://openalex.org/W2109726592","https://openalex.org/W2120043163","https://openalex.org/W2127048411","https://openalex.org/W2128366083","https://openalex.org/W2147230903","https://openalex.org/W2151936673","https://openalex.org/W2160220393"],"related_works":["https://openalex.org/W2963285371","https://openalex.org/W2588799191","https://openalex.org/W2551034774","https://openalex.org/W3104778713","https://openalex.org/W1964108907","https://openalex.org/W2963666952","https://openalex.org/W3153719637","https://openalex.org/W2075846943","https://openalex.org/W1551221054","https://openalex.org/W2559967722","https://openalex.org/W2564281782","https://openalex.org/W1847242552","https://openalex.org/W2154256239","https://openalex.org/W2942156587","https://openalex.org/W2950823092","https://openalex.org/W2167946976","https://openalex.org/W2400484107","https://openalex.org/W2282495428","https://openalex.org/W3171990983","https://openalex.org/W2998531422"],"abstract_inverted_index":{"We":[0],"derive":[1],"rigorous":[2,247],"bounds":[3,272],"for":[4,11],"well-defined":[5,98,157],"community":[6,121],"structure":[7,99,158,215,259],"in":[8,54,94,102,152,175,181,206,225],"complex":[9],"networks":[10],"a":[12,41,44,55,127,193,203,218],"stochastic":[13],"block":[14],"model":[15],"(SBM)":[16],"benchmark.":[17],"In":[18],"particular,":[19],"we":[20,81,107,250],"analyse":[21],"the":[22,64,73,76,83,95,153,176,182,190,207,237,240,246,265,274],"effect":[23],"of":[24,66,75,78,120,239,267],"inter-community":[25],"\u2018noise\u2019":[26],"(inter-community":[27],"edges)":[28],"on":[29,63,72,85,253,273],"any":[30,67],"\u2018community":[31,144],"detection\u2019":[32,145],"algorithm's":[33],"ability":[34],"to":[35,40,50,91,114,125,137,197],"correctly":[36],"group":[37],"nodes":[38],"assigned":[39],"planted":[42],"partition,":[43],"problem":[45,84],"which":[46,221],"has":[47,212],"been":[48],"proved":[49],"be":[51,112,223],"NP":[52],"complete":[53],"standard":[56],"rendition.":[57],"Our":[58],"result":[59],"does":[60],"not":[61],"rely":[62],"use":[65],"one":[68],"particular":[69],"algorithm":[70],"nor":[71],"analysis":[74],"limitations":[77],"inference.":[79],"Rather,":[80],"turn":[82],"its":[86,187],"head":[87],"and":[88,139,159,179,260],"work":[89],"backwards":[90],"examine":[92],"when,":[93],"first":[96],"place,":[97],"may":[100],"exist":[101],"SBMs.":[103],"The":[104,118],"method":[105],"that":[106,150,164,233,249],"introduce":[108],"here":[109,252],"could":[110],"potentially":[111],"applied":[113],"other":[115,140],"computational":[116,231],"problems.":[117],"objective":[119],"detection":[122],"algorithms":[123,270],"is":[124,165,195],"partition":[126,163,194,220],"given":[128],"network":[129,204],"into":[130,170],"optimally":[131],"disjoint":[132],"subgraphs":[133],"(or":[134],"communities).":[135],"Similar":[136],"|$k$|-SAT":[138],"combinatorial":[141],"optimization":[142],"problems,":[143],"exhibits":[146],"different":[147],"phases.":[148],"Networks":[149],"lie":[151],"\u2018unsolvable":[154],"phase\u2019":[155],"lack":[156],"thus":[160],"have":[161,256],"no":[162],"meaningful.":[166],"Solvable":[167],"systems":[168],"splinter":[169],"two":[171],"disparate":[172],"phases:":[173],"those":[174,180],"\u2018hard\u2019":[177],"phase":[178],"\u2018easy\u2019":[183],"phase.":[184,276],"As":[185],"befits":[186],"name,":[188],"within":[189],"easy":[191,196],"phase,":[192,209],"achieve":[198],"by":[199],"known":[200],"algorithms.":[201],"When":[202,242],"lies":[205],"hard":[208,275],"it":[210],"still":[211],"an":[213,229,257],"underlying":[214,258],"yet,":[216],"finding":[217],"meaningful":[219],"can":[222],"checked":[224],"polynomial":[226],"time":[227],"requires":[228],"exhaustive":[230],"effort":[232],"rapidly":[234],"increases":[235],"with":[236],"size":[238],"graph.":[241],"taken":[243],"together,":[244],"(i)":[245],"results":[248,263],"report":[251],"when":[254],"graphs":[255],"(ii)":[261],"recent":[262],"concerning":[264],"limits":[266],"rather":[268],"general":[269],"suggest":[271]},"counts_by_year":[],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2022-10-05T00:00:00"}