{"id":"https://openalex.org/W2067247412","doi":"https://doi.org/10.1080/10586458.2001.10504428","title":"A Random Graph Model for Power Law Graphs","display_name":"A Random Graph Model for Power Law Graphs","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2067247412","doi":"https://doi.org/10.1080/10586458.2001.10504428","mag":"2067247412"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2001.10504428","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504428","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2001.10504428","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"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":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2001.10504428","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018122508","display_name":"William Aiello","orcid":null},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]},{"id":"https://openalex.org/I4210098935","display_name":"Li Creative Technologies (United States)","ror":"https://ror.org/010hpfk35","country_code":"US","type":"company","lineage":["https://openalex.org/I4210098935"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William Aiello","raw_affiliation_strings":["AT&T Labs, 180 Park Avenue, Florham Park, NJ, 07932, United States E-mail: aiello@research.att.com","AT&T Labs , 180 Park Avenue, Florham Park , NJ , 07932 , United States E-mail: aiello@research.att.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AT&T Labs, 180 Park Avenue, Florham Park, NJ, 07932, United States E-mail: aiello@research.att.com","institution_ids":["https://openalex.org/I4210098935"]},{"raw_affiliation_string":"AT&T Labs , 180 Park Avenue, Florham Park , NJ , 07932 , United States E-mail: aiello@research.att.com","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113657664","display_name":"Fan Chung","orcid":"https://orcid.org/0000-0002-6553-7402"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fan Chung","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112, United States E-mail: fan@ucsd.edu","Department of Mathematics , University of California , San Diego, 9500 Gilman Drive, La Jolla , CA , 92093-0112 , United States E-mail: fan@ucsd.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112, United States E-mail: fan@ucsd.edu","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Department of Mathematics , University of California , San Diego, 9500 Gilman Drive, La Jolla , CA , 92093-0112 , United States E-mail: fan@ucsd.edu","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036596371","display_name":"Linyuan L\u00fc","orcid":"https://orcid.org/0000-0003-0155-2002"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Linyuan Lu","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112, United States E-mail: llu@euclid.ucsd.edu","Department of Mathematics , University of California , San Diego, 9500 Gilman Drive, La Jolla , CA , 92093-0112 , United States E-mail: llu@euclid.ucsd.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112, United States E-mail: llu@euclid.ucsd.edu","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Department of Mathematics , University of California , San Diego, 9500 Gilman Drive, La Jolla , CA , 92093-0112 , United States E-mail: llu@euclid.ucsd.edu","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.0835,"has_fulltext":true,"cited_by_count":425,"citation_normalized_percentile":{"value":0.98013868,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"10","issue":"1","first_page":"53","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11476","display_name":"Graph theory and applications","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.834757387638092},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7181714773178101},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.5922866463661194},{"id":"https://openalex.org/keywords/preferential-attachment","display_name":"Preferential attachment","score":0.5303305387496948},{"id":"https://openalex.org/keywords/giant-component","display_name":"Giant component","score":0.5161946415901184},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5086230039596558},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5011959075927734},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.4710697531700134},{"id":"https://openalex.org/keywords/block-graph","display_name":"Block graph","score":0.46026211977005005},{"id":"https://openalex.org/keywords/random-geometric-graph","display_name":"Random geometric graph","score":0.4558474123477936},{"id":"https://openalex.org/keywords/power-law","display_name":"Power law","score":0.44864991307258606},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4065101444721222},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3978586792945862},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.3630245625972748},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.20966067910194397},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.17888623476028442},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1554490625858307},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.14171478152275085}],"concepts":[{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.834757387638092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7181714773178101},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.5922866463661194},{"id":"https://openalex.org/C2780600066","wikidata":"https://www.wikidata.org/wiki/Q7239828","display_name":"Preferential attachment","level":3,"score":0.5303305387496948},{"id":"https://openalex.org/C148818006","wikidata":"https://www.wikidata.org/wiki/Q4137985","display_name":"Giant component","level":4,"score":0.5161946415901184},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5086230039596558},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5011959075927734},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.4710697531700134},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.46026211977005005},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.4558474123477936},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.44864991307258606},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4065101444721222},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3978586792945862},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.3630245625972748},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.20966067910194397},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.17888623476028442},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1554490625858307},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.14171478152275085}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1080/10586458.2001.10504428","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504428","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2001.10504428","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"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":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/999188420","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/999188420","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:10.1.1.17.213","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.213","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-cse.ucsd.edu/users/fan/research/papers/random.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.18.287","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.287","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-cse.ucsd.edu/users/fan/research/papers/Random_graph.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.30.6827","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.6827","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucsd.edu/~fan/power.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.63.871","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.871","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucsd.edu/~llu/papers/power.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.8156","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.8156","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucsd.edu/~llu/papers/power.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.80.6819","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.6819","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucsd.edu/~fan/random.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1080/10586458.2001.10504428","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2001.10504428","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/10586458.2001.10504428","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"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":"Experimental Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.4099999964237213}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2067247412.pdf","grobid_xml":"https://content.openalex.org/works/W2067247412.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W358088974","https://openalex.org/W1592213313","https://openalex.org/W1660264423","https://openalex.org/W1976969221","https://openalex.org/W2008620264","https://openalex.org/W2039990322","https://openalex.org/W2044881936","https://openalex.org/W2068871408","https://openalex.org/W2097147952","https://openalex.org/W2115579680","https://openalex.org/W2117495845","https://openalex.org/W2124250275","https://openalex.org/W2129620481","https://openalex.org/W2129918926","https://openalex.org/W2134122907","https://openalex.org/W2146162554","https://openalex.org/W2151626491","https://openalex.org/W2769133055","https://openalex.org/W2997134027","https://openalex.org/W4231102428"],"related_works":["https://openalex.org/W2130919150","https://openalex.org/W4248914732","https://openalex.org/W4252484501","https://openalex.org/W2290279467","https://openalex.org/W4313053968","https://openalex.org/W2895909952","https://openalex.org/W2990383345","https://openalex.org/W2119340943","https://openalex.org/W4319079309","https://openalex.org/W2963685758"],"abstract_inverted_index":{"We":[0,89,108],"propose":[1],"a":[2,8,20,27],"random":[3,121],"graph":[4,55],"model":[5,24,95],"which":[6,18,82],"is":[7],"special":[9],"case":[10],"of":[11,30,45,53,65,75,78,93,99,120],"sparserandom":[12],"graphs":[13,102,122],"with":[14,86,96],"given":[15],"degree":[16],"sequences":[17],"satisfy":[19],"power":[21],"law.":[22],"This":[23],"involves":[25],"only":[26],"small":[28],"number":[29],"paramo":[31],"eters,":[32],"called":[33],"logsize":[34],"and":[35,117],"log-log":[36],"growth":[37],"rate.":[38],"These":[39],"parameters":[40],"capture":[41],"some":[42,100],"universal":[43],"characteristics":[44],"massive":[46,101],"graphs.":[47],"From":[48],"these":[49],"parameters,":[50,67],"various":[51],"properties":[52],"the":[54,66,72,76,79,91,97,111,114,118],"can":[56],"be":[57],"derived.":[58],"For":[59],"example,":[60],"for":[61],"certai":[62],"n":[63],"ranges":[64],"we":[68],"wi":[69],"II":[70],"compute":[71],"expected":[73],"distribution":[74],"sizes":[77],"connected":[80],"components":[81],"almost":[83],"surely":[84],"occur":[85],"high":[87],"probability.":[88],"illustrate":[90],"consistency":[92],"our":[94],"behavior":[98],"derived":[103],"from":[104],"data":[105],"in":[106,123],"telecommunications.":[107],"also":[109],"discuss":[110],"threshold":[112],"function,":[113],"giant":[115],"component,":[116],"evolution":[119],"this":[124],"model.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":28},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":25},{"year":2014,"cited_by_count":31},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":19}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}