{"id":"https://openalex.org/W2162426050","doi":"https://doi.org/10.1017/s096354830600753x","title":"Distribution of Vertex Degree in Web-Graphs","display_name":"Distribution of Vertex Degree in Web-Graphs","publication_year":2006,"publication_date":"2006-07-31","ids":{"openalex":"https://openalex.org/W2162426050","doi":"https://doi.org/10.1017/s096354830600753x","mag":"2162426050"},"language":"en","primary_location":{"id":"doi:10.1017/s096354830600753x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354830600753x","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5022238950","display_name":"Colin Cooper","orcid":"https://orcid.org/0000-0002-5264-4401"},"institutions":[{"id":"https://openalex.org/I124357947","display_name":"University of London","ror":"https://ror.org/04cw6st05","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947"]},{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"COLIN COOPER","raw_affiliation_strings":["Department of Computer Science, King's College, University of London, London WC2R 2LS, UK (e-mail:","Department of Computer Science, King's College, University of London, London WC2R 2LS, UK (e-mail: colin.cooper@kcl.ac.uk)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, King's College, University of London, London WC2R 2LS, UK (e-mail:","institution_ids":["https://openalex.org/I183935753"]},{"raw_affiliation_string":"Department of Computer Science, King's College, University of London, London WC2R 2LS, UK (e-mail: colin.cooper@kcl.ac.uk)","institution_ids":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022238950"],"corresponding_institution_ids":["https://openalex.org/I124357947","https://openalex.org/I183935753"],"apc_list":null,"apc_paid":null,"fwci":0.8965,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.74884619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"5","first_page":"637","last_page":"661"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9991999864578247,"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/T11716","display_name":"Random Matrices and Applications","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/combinatorics","display_name":"Combinatorics","score":0.7264178395271301},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6402572393417358},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.6402146220207214},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.6044800877571106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5898169279098511},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.5241518020629883},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5142406821250916},{"id":"https://openalex.org/keywords/preferential-attachment","display_name":"Preferential attachment","score":0.5045896768569946},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48603516817092896},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44881337881088257},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.44002532958984375},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.10045653581619263},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07032319903373718}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7264178395271301},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6402572393417358},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.6402146220207214},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.6044800877571106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5898169279098511},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.5241518020629883},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5142406821250916},{"id":"https://openalex.org/C2780600066","wikidata":"https://www.wikidata.org/wiki/Q7239828","display_name":"Preferential attachment","level":3,"score":0.5045896768569946},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48603516817092896},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44881337881088257},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.44002532958984375},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.10045653581619263},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07032319903373718},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1017/s096354830600753x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354830600753x","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.127.7790","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.7790","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/~af1p/Teaching/WWW2004/DegDistn_CPC.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.14.8018","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.8018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.kcl.ac.uk/staff/ccooper/store/DegDistn_HA.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.144.3053","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.144.3053","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.kcl.ac.uk/staff/ccooper/papers/webg_DegDistn.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.144.457","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.144.457","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.kcl.ac.uk/staff/ccooper/papers/DegDistn_HA.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.62.5386","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.5386","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.kcl.ac.uk/staff/ccooper/store/DegDistn.pdf","raw_type":"text"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/373a9891-836b-4ab9-ab11-e798e0df65d9","is_oa":false,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/373a9891-836b-4ab9-ab11-e798e0df65d9","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cooper , C 2006 , ' Distribution of vertex degree in web-graphs ' , Combinatorics, Probability and Computing , vol. 15 , no. 5 , pp. 637 - 661 . https://doi.org/10.1017/S096354830600753X","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W207687955","https://openalex.org/W1976969221","https://openalex.org/W1981086745","https://openalex.org/W1984137208","https://openalex.org/W2008620264","https://openalex.org/W2048324994","https://openalex.org/W2056380633","https://openalex.org/W2061118827","https://openalex.org/W2075946320","https://openalex.org/W2115579680","https://openalex.org/W2135869163","https://openalex.org/W2138621811","https://openalex.org/W2175110005","https://openalex.org/W2989661724","https://openalex.org/W2997134027"],"related_works":["https://openalex.org/W1560913374","https://openalex.org/W2141185052","https://openalex.org/W230111105","https://openalex.org/W2341322822","https://openalex.org/W2976337371","https://openalex.org/W1981257001","https://openalex.org/W2922108232","https://openalex.org/W3101672529","https://openalex.org/W3013262114","https://openalex.org/W212696416"],"abstract_inverted_index":{"We":[0],"give":[1,66],"results":[2,68],"for":[3,59,69],"the":[4,18,38,42,53,60,70],"age-dependent":[5],"distribution":[6],"of":[7,12,14,41,45],"vertex":[8],"degree":[9,16],"and":[10,74],"number":[11,44],"vertices":[13],"given":[15],"in":[17,28],"undirected":[19,61,76],"web-graph":[20],"process,":[21,73],"a":[22],"discrete":[23],"random":[24],"graph":[25],"process":[26,62],"introduced":[27],"[8].":[29],"For":[30],"such":[31],"processes":[32],"we":[33],"show":[34],"that":[35],"as":[36],"is":[37],"limiting":[39],"ratio":[40],"expected":[43,54],"edge":[46],"endpoints":[47],"inserted":[48],"by":[49],"preferential":[50],"attachment":[51],"to":[52,65],"total":[55],"degree.":[56],"The":[57],"proof":[58],"generalizes":[63],"naturally":[64],"similar":[67],"directed":[71],"hub-authority":[72],"an":[75],"hypergraph":[77],"process.":[78]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
