{"id":"https://openalex.org/W2096143162","doi":"https://doi.org/10.1109/tpami.1980.4767033","title":"Random Graphs: Structural-Contextual Dichotomy","display_name":"Random Graphs: Structural-Contextual Dichotomy","publication_year":1980,"publication_date":"1980-07-01","ids":{"openalex":"https://openalex.org/W2096143162","doi":"https://doi.org/10.1109/tpami.1980.4767033","mag":"2096143162","pmid":"https://pubmed.ncbi.nlm.nih.gov/21868910"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.1980.4767033","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1980.4767033","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5051841038","display_name":"Andrew K. C. Wong","orcid":"https://orcid.org/0000-0002-0019-7152"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Andrew K. C. Wong","raw_affiliation_strings":["MEMBER, IEEE, Department of Systems Design, University of Waterloo, Waterloo, Ont., Canada","MEMBER, IEEE, Department of Systems Design, University of Waterloo, Waterloo, Ont., Canada.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MEMBER, IEEE, Department of Systems Design, University of Waterloo, Waterloo, Ont., Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"MEMBER, IEEE, Department of Systems Design, University of Waterloo, Waterloo, Ont., Canada.#TAB#","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084261042","display_name":"David E. Ghahraman","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David E. Ghahraman","raw_affiliation_strings":["Carnegie Institute of Technology, Carnegie Mellon University, Pittsburgh, PA, USA","MEMBER, IEEE, Institute of Technology, Carnegie-Mellon University, Pittsburgh, PA 15213; Megatest Corporation, Santa Clara, CA.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Institute of Technology, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"MEMBER, IEEE, Institute of Technology, Carnegie-Mellon University, Pittsburgh, PA 15213; Megatest Corporation, Santa Clara, CA.#TAB#","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.885,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"PAMI-2","issue":"4","first_page":"341","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9611999988555908,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.7066053748130798},{"id":"https://openalex.org/keywords/outcome","display_name":"Outcome (game theory)","score":0.5720124840736389},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4874849319458008},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.4720105826854706},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.43377625942230225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4327414631843567},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41302067041397095},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.4100203812122345},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4004521369934082},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3770435154438019},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.370281457901001},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.31607377529144287},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17664843797683716},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.10256069898605347}],"concepts":[{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.7066053748130798},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.5720124840736389},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4874849319458008},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.4720105826854706},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.43377625942230225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4327414631843567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41302067041397095},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.4100203812122345},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4004521369934082},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3770435154438019},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.370281457901001},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31607377529144287},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17664843797683716},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.10256069898605347},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":2,"locations":[{"id":"doi:10.1109/tpami.1980.4767033","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1980.4767033","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:21868910","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21868910","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":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W41728724","https://openalex.org/W82276609","https://openalex.org/W1520376281","https://openalex.org/W1552744309","https://openalex.org/W1608549080","https://openalex.org/W1655990431","https://openalex.org/W1987179556","https://openalex.org/W2021930057","https://openalex.org/W2026740477","https://openalex.org/W2027417898","https://openalex.org/W2038525388","https://openalex.org/W2045798786","https://openalex.org/W2066587267","https://openalex.org/W2084134149","https://openalex.org/W2087435614","https://openalex.org/W2094139270","https://openalex.org/W2121053863","https://openalex.org/W2150985179","https://openalex.org/W3144287057","https://openalex.org/W4299807969","https://openalex.org/W6601725199","https://openalex.org/W6631249596","https://openalex.org/W6636172856","https://openalex.org/W6682059559"],"related_works":["https://openalex.org/W3041490575","https://openalex.org/W4299994946","https://openalex.org/W2970690932","https://openalex.org/W4321135767","https://openalex.org/W2952239832","https://openalex.org/W1560044520","https://openalex.org/W2567996374","https://openalex.org/W2069619724","https://openalex.org/W4390575946","https://openalex.org/W2479670578"],"abstract_inverted_index":{"A":[0],"formal":[1],"definition":[2,17],"of":[3,26,31,39,48,79,87,105],"random":[4,27,89,93,113],"graphs":[5,33,53,86,108],"is":[6,9,18,34,95],"introduced":[7],"which":[8],"applicable":[10],"to":[11,20,44,58,65,97,111],"graphical":[12],"pattern":[13],"recognition":[14],"problems.":[15],"The":[16,29,74,91],"used":[19,96],"formulate":[21],"rigorously":[22],"the":[23,37,45,51,55,67,99,106,112],"structural-contextual":[24],"dichotomy":[25],"graphs.":[28],"probability":[30],"outcome":[32,52,85,107],"expressed":[35],"as":[36,84],"product":[38],"two":[40],"terms,":[41],"one":[42],"due":[43,57],"statistical":[46],"variability":[47],"structure":[49],"among":[50],"and":[54,71,102],"other":[56],"their":[59],"contextual":[60],"variability.":[61],"Expressions":[62],"are":[63,82],"obtained":[64],"estimate":[66],"various":[68],"probability,":[69],"typicality,":[70],"entropy":[72],"measures.":[73],"members":[75],"in":[76],"an":[77],"ensemble":[78],"signed":[80],"digraphs":[81],"interpreted":[83],"a":[88],"graph.":[90,114],"synthesized":[92],"graph":[94],"quantify":[98],"structural,":[100],"contextual,":[101],"overall":[103],"typicality":[104],"with":[109],"respect":[110]},"counts_by_year":[{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}