{"id":"https://openalex.org/W4237656870","doi":"https://doi.org/10.1080/15427951.2007.10129137","title":"A Geometric Preferential Attachment Model of Networks II","display_name":"A Geometric Preferential Attachment Model of Networks II","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W4237656870","doi":"https://doi.org/10.1080/15427951.2007.10129137"},"language":"en","primary_location":{"id":"doi:10.1080/15427951.2007.10129137","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129137","pdf_url":"https://www.internetmathematicsjournal.com/article/1434.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/1434.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055212893","display_name":"Abraham D. Flaxman","orcid":"https://orcid.org/0000-0001-6033-4713"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abraham D. Flaxman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan M. Frieze","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002345780","display_name":"Juan C. Vera","orcid":"https://orcid.org/0000-0003-1394-3422"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Juan Vera","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5848,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.83856292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"4","issue":"1","first_page":"87","last_page":"111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.998199999332428,"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":0.998199999332428,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9979000091552734,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8168812990188599},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7387055158615112},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5142056941986084},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.49481385946273804},{"id":"https://openalex.org/keywords/random-geometric-graph","display_name":"Random geometric graph","score":0.47007447481155396},{"id":"https://openalex.org/keywords/preferential-attachment","display_name":"Preferential attachment","score":0.46640315651893616},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.4449978768825531},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3479281961917877},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14277148246765137},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.09552440047264099},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.09368985891342163}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8168812990188599},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7387055158615112},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5142056941986084},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.49481385946273804},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.47007447481155396},{"id":"https://openalex.org/C2780600066","wikidata":"https://www.wikidata.org/wiki/Q7239828","display_name":"Preferential attachment","level":3,"score":0.46640315651893616},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.4449978768825531},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3479281961917877},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14277148246765137},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.09552440047264099},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.09368985891342163}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/15427951.2007.10129137","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129137","pdf_url":"https://www.internetmathematicsjournal.com/article/1434.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/1243430569","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.im/1243430569","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"}],"best_oa_location":{"id":"doi:10.1080/15427951.2007.10129137","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129137","pdf_url":"https://www.internetmathematicsjournal.com/article/1434.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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6899999976158142}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4237656870.pdf","grobid_xml":"https://content.openalex.org/works/W4237656870.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W207687955","https://openalex.org/W630423399","https://openalex.org/W1568371145","https://openalex.org/W1572923654","https://openalex.org/W1591378753","https://openalex.org/W1741787210","https://openalex.org/W1977585052","https://openalex.org/W1987236914","https://openalex.org/W1993803315","https://openalex.org/W1994840070","https://openalex.org/W2008620264","https://openalex.org/W2016743875","https://openalex.org/W2019789576","https://openalex.org/W2021289261","https://openalex.org/W2056380633","https://openalex.org/W2057444879","https://openalex.org/W2061118827","https://openalex.org/W2097147952","https://openalex.org/W2115579680","https://openalex.org/W2129620481","https://openalex.org/W2151626491","https://openalex.org/W2152361742","https://openalex.org/W2156950966","https://openalex.org/W3030115066","https://openalex.org/W4230202685","https://openalex.org/W4230526081","https://openalex.org/W4234808307","https://openalex.org/W4242291765","https://openalex.org/W4244446631","https://openalex.org/W4250244821","https://openalex.org/W4392733169"],"related_works":["https://openalex.org/W2608806994","https://openalex.org/W2132287883","https://openalex.org/W4299783662","https://openalex.org/W2583831198","https://openalex.org/W2187055990","https://openalex.org/W2130919150","https://openalex.org/W4252484501","https://openalex.org/W3003396734","https://openalex.org/W2162752950","https://openalex.org/W2951136563"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,23,36],"random":[3,14,65],"graph":[4,24],"_G_<sub>":[5,45],"<em>n</em>":[6,46,60],"</sub>":[7,47],"that":[8],"combines":[9],"certain":[10],"aspects":[11],"of":[12,39,44],"geometric":[13],"graphs":[15],"and":[16],"preferential":[17],"attachment":[18],"graphs.":[19],"This":[20],"model":[21],"yields":[22],"with":[25],"power":[26],"law":[27],"degree":[28],"distribution":[29],"where":[30],"the":[31,40,67],"expansion":[32],"property":[33],"depends":[34],"on":[35],"tunable":[37],"parameter":[38],"model.":[41],"The":[42],"vertices":[43],"are":[48],"_n_":[49],"sequentially":[50],"generated":[51],"points,":[52],"_x_<sub>1</sub>,":[53,87],"_x_<sub>2</sub>,":[54,88],".":[55,56,57,89,90,91],",":[58,92],"_x_<sub>":[59,74,93],"</sub>,":[61,76],"chosen":[62],"uniformly":[63],"at":[64],"from":[66,84],"unit":[68],"sphere":[69],"in":[70],"R<sup>3</sup>":[71],"After":[72],"generating":[73],"<em>t</em>":[75],"we":[77],"randomly":[78],"connect":[79],"it":[80],"to":[81],"_m_":[82],"points":[83,86],"those":[85],"<em>t</em>\u22121</sub>.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}