{"id":"https://openalex.org/W3119733817","doi":"https://doi.org/10.3390/e23010065","title":"Exact Recovery of Stochastic Block Model by Ising Model","display_name":"Exact Recovery of Stochastic Block Model by Ising Model","publication_year":2021,"publication_date":"2021-01-02","ids":{"openalex":"https://openalex.org/W3119733817","doi":"https://doi.org/10.3390/e23010065","mag":"3119733817","pmid":"https://pubmed.ncbi.nlm.nih.gov/33401691"},"language":"en","primary_location":{"id":"doi:10.3390/e23010065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010065","pdf_url":"https://www.mdpi.com/1099-4300/23/1/65/pdf?version=1610109198","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/1/65/pdf?version=1610109198","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101578615","display_name":"Zhao Feng","orcid":"https://orcid.org/0000-0003-3907-9556"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Zhao","raw_affiliation_strings":["Department of Electronics, Tsinghua University, Beijing 100084, China"],"raw_orcid":"https://orcid.org/0000-0003-3907-9556","affiliations":[{"raw_affiliation_string":"Department of Electronics, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100725244","display_name":"Min Ye","orcid":"https://orcid.org/0000-0003-1351-8880"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Min Ye","raw_affiliation_strings":["Tsinghua Berkeley Shenzhen Institute, Berkeley, CA 94704, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua Berkeley Shenzhen Institute, Berkeley, CA 94704, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088293566","display_name":"Shao\u2010Lun Huang","orcid":"https://orcid.org/0000-0003-2827-4022"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shao-Lun Huang","raw_affiliation_strings":["Tsinghua Berkeley Shenzhen Institute, Berkeley, CA 94704, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua Berkeley Shenzhen Institute, Berkeley, CA 94704, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088293566"],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.3479,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.53336006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"23","issue":"1","first_page":"65","last_page":"65"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":1.0,"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":1.0,"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":0.9994000196456909,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/ising-model","display_name":"Ising model","score":0.7064988017082214},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7064459919929504},{"id":"https://openalex.org/keywords/stochastic-block-model","display_name":"Stochastic block model","score":0.683205246925354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6359041333198547},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4887659549713135},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39801061153411865},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.2524850070476532},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10339072346687317},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0761134922504425}],"concepts":[{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.7064988017082214},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7064459919929504},{"id":"https://openalex.org/C2779982251","wikidata":"https://www.wikidata.org/wiki/Q25053762","display_name":"Stochastic block model","level":3,"score":0.683205246925354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6359041333198547},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4887659549713135},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39801061153411865},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2524850070476532},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10339072346687317},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0761134922504425},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23010065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010065","pdf_url":"https://www.mdpi.com/1099-4300/23/1/65/pdf?version=1610109198","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33401691","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33401691","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:d7bf1e71ec2b4f4ba2961ea40f53b8a6","is_oa":true,"landing_page_url":"https://doaj.org/article/d7bf1e71ec2b4f4ba2961ea40f53b8a6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 1, p 65 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/1/65/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23010065","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 23; Issue 1; Pages: 65","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7823472","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7823472","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23010065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010065","pdf_url":"https://www.mdpi.com/1099-4300/23/1/65/pdf?version=1610109198","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6483256435","display_name":null,"funder_award_id":"61807021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3119733817.pdf","grobid_xml":"https://content.openalex.org/works/W3119733817.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W2012369610","https://openalex.org/W2014441733","https://openalex.org/W2019473674","https://openalex.org/W2036116799","https://openalex.org/W2047940964","https://openalex.org/W2056760934","https://openalex.org/W2065309575","https://openalex.org/W2068674173","https://openalex.org/W2074724691","https://openalex.org/W2102907934","https://openalex.org/W2127048411","https://openalex.org/W2137531873","https://openalex.org/W2144799688","https://openalex.org/W2159793005","https://openalex.org/W2219655028","https://openalex.org/W2302206641","https://openalex.org/W2416738288","https://openalex.org/W2567866584","https://openalex.org/W2602671714","https://openalex.org/W2613215434","https://openalex.org/W2765742625","https://openalex.org/W2799906818","https://openalex.org/W2962704236","https://openalex.org/W2963264680","https://openalex.org/W2963685135","https://openalex.org/W3016050978","https://openalex.org/W3098833389","https://openalex.org/W3102641634","https://openalex.org/W3143219376","https://openalex.org/W3203254448","https://openalex.org/W6735855921"],"related_works":["https://openalex.org/W4386952843","https://openalex.org/W2744148269","https://openalex.org/W3016050978","https://openalex.org/W4245953108","https://openalex.org/W1977619534","https://openalex.org/W2236763869","https://openalex.org/W2097626286","https://openalex.org/W4293568347","https://openalex.org/W2808230936","https://openalex.org/W2023659367"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,28,63,84],"study":[4],"the":[5,25,35,39,53,70,74,90,95],"phase":[6,96],"transition":[7,97],"property":[8],"of":[9,56,73],"an":[10,48,65],"Ising":[11,26],"model":[12,21,71],"defined":[13],"on":[14,24],"a":[15,30],"special":[16,54],"random":[17],"graph-the":[18],"stochastic":[19,31,42,91],"block":[20],"(SBM).":[22],"Based":[23],"model,":[27],"propose":[29],"estimator":[32,68,92],"to":[33,88],"achieve":[34],"exact":[36],"recovery":[37],"for":[38,69],"SBM.":[40],"The":[41],"algorithm":[43],"can":[44,77],"be":[45,78],"transformed":[46],"into":[47],"optimization":[49],"problem,":[50],"which":[51,76],"includes":[52],"case":[55],"maximum":[57,60],"likelihood":[58],"and":[59,93],"modularity.":[61],"Additionally,":[62],"give":[64],"unbiased":[66],"convergent":[67],"parameters":[72],"SBM,":[75],"computed":[79],"in":[80],"constant":[81],"time.":[82],"Finally,":[83],"use":[85],"metropolis":[86],"sampling":[87],"realize":[89],"verify":[94],"phenomenon":[98],"thfough":[99],"experiments.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}