{"id":"https://openalex.org/W1990495065","doi":"https://doi.org/10.1080/15427951.2008.10129301","title":"Directed Random Dot Product Graphs","display_name":"Directed Random Dot Product Graphs","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1990495065","doi":"https://doi.org/10.1080/15427951.2008.10129301","mag":"1990495065"},"language":"en","primary_location":{"id":"doi:10.1080/15427951.2008.10129301","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129301","pdf_url":"https://www.internetmathematicsjournal.com/article/1450.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.internetmathematicsjournal.com/article/1450.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001785077","display_name":"Stephen J. Young","orcid":"https://orcid.org/0000-0003-0582-6787"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stephen J. Young","raw_affiliation_strings":["Georgia Institute of Technology, School of Mathematics, 686 Cherry Street, Atlanta, GA 30332"],"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, School of Mathematics, 686 Cherry Street, Atlanta, GA 30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060189138","display_name":"Edward Scheinerman","orcid":"https://orcid.org/0000-0003-4124-7838"},"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 Scheinerman","raw_affiliation_strings":["Whiting School of Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218"],"affiliations":[{"raw_affiliation_string":"Whiting School of Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001785077"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":1.2348,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.79524532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"5","issue":"1-2","first_page":"91","last_page":"111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7594573497772217},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6686036586761475},{"id":"https://openalex.org/keywords/dot-product","display_name":"Dot product","score":0.6144174933433533},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6109101176261902},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5968765616416931},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5211420059204102},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5063284635543823},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4856235086917877},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.48549774289131165},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3575940430164337},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.20044896006584167},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19333100318908691},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11793941259384155},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.08885407447814941},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07948827743530273}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7594573497772217},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6686036586761475},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.6144174933433533},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6109101176261902},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5968765616416931},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5211420059204102},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5063284635543823},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4856235086917877},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.48549774289131165},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3575940430164337},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.20044896006584167},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19333100318908691},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11793941259384155},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.08885407447814941},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07948827743530273},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/15427951.2008.10129301","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129301","pdf_url":"https://www.internetmathematicsjournal.com/article/1450.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.im/1259158599","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.im/1259158599","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.145.3892","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.3892","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.gatech.edu/~young/research/papers/InnerProductGraph.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1080/15427951.2008.10129301","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2008.10129301","pdf_url":"https://www.internetmathematicsjournal.com/article/1450.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1990495065.pdf","grobid_xml":"https://content.openalex.org/works/W1990495065.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W160364443","https://openalex.org/W1526841711","https://openalex.org/W1541172283","https://openalex.org/W1568307856","https://openalex.org/W1592356192","https://openalex.org/W1976625337","https://openalex.org/W1981086745","https://openalex.org/W2021680564","https://openalex.org/W2038550366","https://openalex.org/W2040956707","https://openalex.org/W2053248591","https://openalex.org/W2063639254","https://openalex.org/W2074061376","https://openalex.org/W2107648668","https://openalex.org/W2108614537","https://openalex.org/W2120511087","https://openalex.org/W2124637492","https://openalex.org/W2128678576","https://openalex.org/W2560229363","https://openalex.org/W2770485470","https://openalex.org/W2950924954","https://openalex.org/W2953204146","https://openalex.org/W3030115066","https://openalex.org/W3103899801","https://openalex.org/W4300223101","https://openalex.org/W4388297583"],"related_works":["https://openalex.org/W4293160469","https://openalex.org/W2963945385","https://openalex.org/W2146137903","https://openalex.org/W1587202469","https://openalex.org/W2619014136","https://openalex.org/W2256700515","https://openalex.org/W2013497788","https://openalex.org/W2894884315","https://openalex.org/W2013285130","https://openalex.org/W2080844985"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"three":[5],"models":[6,25,38],"for":[7],"random":[8,43],"graphs":[9,46,70],"that":[10],"utilize":[11],"the":[12,21,30,42,60,67,77,80],"inner":[13],"product":[14,45],"as":[15],"their":[16,55],"fundamental":[17],"object.":[18],"We":[19,53],"analyze":[20],"behavior":[22,78],"of":[23,69,79],"these":[24,73],"with":[26],"respect":[27],"to":[28,57],"clustering,":[29],"small":[31],"world":[32],"property,":[33],"and":[34,51,75],"degree":[35,81],"distribution.":[36,82],"These":[37],"are":[39],"motivated":[40],"by":[41,48,72],"dot":[44],"developed":[47],"Kraetzl,":[49],"Nickel,":[50],"Scheinerman.":[52],"extend":[54],"results":[56],"fully":[58],"parameterize":[59],"conditions":[61],"under":[62],"which":[63],"clustering":[64],"occurs,":[65],"characterize":[66],"diameter":[68],"generated":[71],"models,":[74],"describe":[76]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}