{"id":"https://openalex.org/W1560044520","doi":"https://doi.org/10.37236/597","title":"On Vertex, Edge, and Vertex-Edge Random Graphs","display_name":"On Vertex, Edge, and Vertex-Edge Random Graphs","publication_year":2011,"publication_date":"2011-05-16","ids":{"openalex":"https://openalex.org/W1560044520","doi":"https://doi.org/10.37236/597","mag":"1560044520"},"language":"en","primary_location":{"id":"doi:10.37236/597","is_oa":true,"landing_page_url":"https://doi.org/10.37236/597","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p110/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p110/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086354431","display_name":"Elizabeth Beer","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elizabeth Beer","raw_affiliation_strings":["Center for Computing Sciences, Bowie, Maryland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computing Sciences, Bowie, Maryland#TAB#","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003190989","display_name":"James Allen Fill","orcid":"https://orcid.org/0000-0003-1023-0398"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Allen Fill","raw_affiliation_strings":["The Johns Hopkins University, Baltimore, Maryland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Johns Hopkins University, Baltimore, Maryland","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022615833","display_name":"Svante Janson","orcid":"https://orcid.org/0000-0002-9680-2790"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Svante Janson","raw_affiliation_strings":["Uppsala University , Uppsala, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Uppsala University , Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112777575","display_name":"Edward R. Scheinerman","orcid":null},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edward R. Scheinerman","raw_affiliation_strings":["The Johns Hopkins University, Baltimore, Maryland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Johns Hopkins University, Baltimore, Maryland","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2397,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.8463217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"18","issue":"1","first_page":"16","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9965000152587891,"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/T11476","display_name":"Graph theory and applications","score":0.9706000089645386,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.7148747444152832},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7113300561904907},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.7112127542495728},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.6742352247238159},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.6178637146949768},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5798261165618896},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5408644080162048},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.5211241841316223},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.4985828399658203},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.4902839958667755},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4866681694984436},{"id":"https://openalex.org/keywords/clique-sum","display_name":"Clique-sum","score":0.4404311776161194},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2637125551700592},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.19186237454414368}],"concepts":[{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.7148747444152832},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7113300561904907},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.7112127542495728},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.6742352247238159},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.6178637146949768},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5798261165618896},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5408644080162048},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.5211241841316223},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.4985828399658203},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.4902839958667755},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4866681694984436},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.4404311776161194},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2637125551700592},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.19186237454414368}],"mesh":[],"locations_count":11,"locations":[{"id":"doi:10.37236/597","is_oa":true,"landing_page_url":"https://doi.org/10.37236/597","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p110/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0812.1410","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0812.1410","pdf_url":"https://arxiv.org/pdf/0812.1410","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":"","raw_type":null},{"id":"mag:2952239832","is_oa":true,"landing_page_url":"https://128.84.21.199/abs/0812.1410?context=math.PR","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:CiteSeerX.psu:10.1.1.148.7678","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.7678","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uu.se/~svante/papers/sj221.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.185.1103","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.1103","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mts.jhu.edu/%7Efill/papers/randomgraphsfull.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.2484","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.2484","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mts.jhu.edu/~fill/papers/randomgraphs.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.231.9072","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.9072","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p110/pdf/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.248.4861","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.4861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0812.1410v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.309.6916","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.6916","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.jhu.edu/~fill/papers/randomgraphsfull.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.0812.1410","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0812.1410","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"},{"id":"mag:1560044520","is_oa":false,"landing_page_url":"https://www.ams.jhu.edu/~fill/papers/randomgraphsfull.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306417669","display_name":"Analytic Algorithmics and Combinatorics","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Analytic Algorithmics and Combinatorics","raw_type":null}],"best_oa_location":{"id":"doi:10.37236/597","is_oa":true,"landing_page_url":"https://doi.org/10.37236/597","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p110/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310145","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95"},{"id":"https://openalex.org/F4320333566","display_name":"National Defense Science and Engineering Graduate","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1560044520.pdf","grobid_xml":"https://content.openalex.org/works/W1560044520.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W630423399","https://openalex.org/W1533473741","https://openalex.org/W1592958377","https://openalex.org/W1986119538","https://openalex.org/W1986955161","https://openalex.org/W1992459191","https://openalex.org/W1993988034","https://openalex.org/W2000297520","https://openalex.org/W2007695797","https://openalex.org/W2029972636","https://openalex.org/W2031211633","https://openalex.org/W2058048823","https://openalex.org/W2066459332","https://openalex.org/W2067951359","https://openalex.org/W2068291241","https://openalex.org/W2082734581","https://openalex.org/W2111754130","https://openalex.org/W2119104742","https://openalex.org/W2138359578","https://openalex.org/W2165064763","https://openalex.org/W2560229363","https://openalex.org/W2905110430","https://openalex.org/W2913927180","https://openalex.org/W2950850272","https://openalex.org/W3143219376"],"related_works":["https://openalex.org/W2567996374","https://openalex.org/W2012853908","https://openalex.org/W2287386204","https://openalex.org/W603403972","https://openalex.org/W2079397350","https://openalex.org/W1514166808","https://openalex.org/W634104060","https://openalex.org/W2963287622","https://openalex.org/W628145248","https://openalex.org/W2963300970","https://openalex.org/W1907987318","https://openalex.org/W2082971831","https://openalex.org/W2913444680","https://openalex.org/W353760616","https://openalex.org/W2108370908","https://openalex.org/W3134695014","https://openalex.org/W2758403374","https://openalex.org/W3034503485","https://openalex.org/W1974893148","https://openalex.org/W2963453289"],"abstract_inverted_index":{"We":[0,65],"consider":[1],"three":[2,43,77],"classes":[3],"of":[4,29,41,45,75],"random":[5,8,11,15,18,22,25,31,35,46,69,86],"graphs:":[6],"edge":[7],"graphs,":[9,12,23,32,70,87],"vertex":[10,24,85],"and":[13,33],"vertex-edge":[14,34,68],"graphs.":[16],"Edge":[17],"graphs":[19,26,36,47],"are":[20,27,93],"Erd\u0151s-R\u00e9nyi":[21],"generalizations":[28],"geometric":[30],"generalize":[37],"both.":[38,64],"The":[39],"names":[40],"these":[42],"types":[44],"describe":[48],"where":[49],"the":[50,53,57,60,72,76,90],"randomness":[51],"in":[52,56,59,63],"models":[54],"lies:":[55],"edges,":[58],"vertices,":[61],"or":[62],"show":[66],"that":[67,89],"ostensibly":[71],"most":[73],"general":[74],"models,":[78],"can":[79],"be":[80],"approximated":[81],"arbitrarily":[82],"closely":[83],"by":[84],"but":[88],"two":[91],"categories":[92],"distinct.":[94]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
