{"id":"https://openalex.org/W2151470713","doi":"https://doi.org/10.1145/1060745.1060827","title":"PageRank as a function of the damping factor","display_name":"PageRank as a function of the damping factor","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2151470713","doi":"https://doi.org/10.1145/1060745.1060827","mag":"2151470713"},"language":"en","primary_location":{"id":"doi:10.1145/1060745.1060827","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1060745.1060827","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th international conference on World Wide Web - WWW '05","raw_type":"proceedings-article"},"type":"conference-abstract","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/A5038842358","display_name":"Paolo Boldi","orcid":"https://orcid.org/0000-0002-8297-6255"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paolo Boldi","raw_affiliation_strings":["Universit\u00e0 degli Studi di Milano"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Milano","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078458093","display_name":"Massimo Santini","orcid":"https://orcid.org/0000-0003-1416-0673"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massimo Santini","raw_affiliation_strings":["Universit\u00e0 degli Studi di Milano"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Milano","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027824085","display_name":"Sebastiano Vigna","orcid":"https://orcid.org/0000-0002-3257-651X"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sebastiano Vigna","raw_affiliation_strings":["Universit\u00e0 degli Studi di Milano"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Milano","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I189158943"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":206,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"557","last_page":"557"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9983000159263611,"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":0.9983000159263611,"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":0.9962999820709229,"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/T11644","display_name":"Spam and Phishing Detection","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/pagerank","display_name":"PageRank","score":0.9652842879295349},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.718482494354248},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6625828742980957},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.5395544767379761},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5181114077568054},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4890170991420746},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44420450925827026},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.43839117884635925},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4341018795967102},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4223192036151886},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.42024335265159607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3803745210170746},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3290640115737915},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27181726694107056},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2471998929977417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.213455468416214},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.12834206223487854},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09252014756202698},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08435919880867004}],"concepts":[{"id":"https://openalex.org/C2779172887","wikidata":"https://www.wikidata.org/wiki/Q184316","display_name":"PageRank","level":2,"score":0.9652842879295349},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.718482494354248},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6625828742980957},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.5395544767379761},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5181114077568054},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4890170991420746},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44420450925827026},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.43839117884635925},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4341018795967102},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4223192036151886},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.42024335265159607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3803745210170746},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3290640115737915},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27181726694107056},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2471998929977417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.213455468416214},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.12834206223487854},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09252014756202698},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08435919880867004},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1060745.1060827","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1060745.1060827","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 14th international conference on World Wide Web - WWW '05","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.59.1496","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.59.1496","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.www2005.org/cdrom/docs/p557.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.76.1767","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.76.1767","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://vigna.dsi.unimi.it/ftp/papers/PageRankAsFunction.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.1730","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.1730","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://vigna.dsi.unimi.it/ftp/papers/PageRankAsFunction.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1520752616","https://openalex.org/W1562405179","https://openalex.org/W1587314265","https://openalex.org/W1764421085","https://openalex.org/W1854214752","https://openalex.org/W1922170032","https://openalex.org/W1981086745","https://openalex.org/W1994727615","https://openalex.org/W2000273502","https://openalex.org/W2014478203","https://openalex.org/W2039976898","https://openalex.org/W2138621811","https://openalex.org/W2147152072","https://openalex.org/W2161118554","https://openalex.org/W2165469059","https://openalex.org/W2169263924","https://openalex.org/W2970618185","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3124338227","https://openalex.org/W2062424259","https://openalex.org/W2324953849","https://openalex.org/W4210608647","https://openalex.org/W4297664343","https://openalex.org/W2951603735","https://openalex.org/W2385963746","https://openalex.org/W2805489503","https://openalex.org/W2376623621","https://openalex.org/W2620111902"],"abstract_inverted_index":{"PageRank":[0,66,104,139,188],"is":[1,13,41,58,91],"defined":[2],"as":[3],"the":[4,17,35,48,63,86,99,148,160,178,182,187,202,205,211],"stationary":[5],"state":[6],"of":[7,34,39,65,85,103,121,141,147,181,195,207,213],"a":[8,22,26,129,166,192],"Markov":[9],"chain.":[10],"The":[11,37,198],"chain":[12],"obtained":[14,190],"by":[15,21,54,175],"perturbing":[16],"transition":[18],"matrix":[19],"induced":[20],"web":[23],"graph":[24],"with":[25,67,154],"damping":[27],"factor":[28],"\u03b1":[29,40,51,72,90,106,122],"that":[30,151,177],"spreads":[31],"uniformly":[32],"part":[33],"rank.":[36],"choice":[38],"eminently":[42],"empirical,":[43],"and":[44,56,144,172],"in":[45,71,78],"most":[46],"cases":[47],"original":[49],"suggestion":[50],"=":[52],"0.85":[53],"Brin":[55],"Page":[57],"still":[59,92],"used.":[60],"Recently,":[61],"however,":[62],"behaviour":[64,174],"respect":[68],"to":[69,75,114,124,210],"changes":[70],"was":[73],"discovered":[74],"be":[76],"useful":[77],"link-spam":[79],"detection[21].":[80],"Moreover,":[81],"an":[82,145],"analytical":[83,173,208],"justification":[84],"value":[87,189],"chosen":[88],"for":[89,117,138,159],"missing.":[93],"In":[94,108],"this":[95],"paper,":[96],"we":[97,110,134,164],"give":[98,128,135],"first":[100],"mathematical":[101],"analysis":[102],"when":[105],"changes.":[107],"particular,":[109],"show":[111,165],"that,":[112],"contrarily":[113],"popular":[115],"belief,":[116],"real-world":[118],"graphs":[119],"values":[120],"close":[123],"1":[125],"do":[126],"not":[127],"more":[130],"meaningful":[131],"ranking.":[132],"Then,":[133],"closed-form":[136],"formulae":[137],"derivatives":[140],"any":[142],"order,":[143],"extension":[146],"Power":[149,183],"Method":[150,184],"approximates":[152],"them":[153],"convergence":[155],"O":[156],"(tk":[157],"\u03b1t)":[158],"k-th":[161,179],"derivative.":[162],"Finally,":[163],"tight":[167],"connection":[168],"between":[169],"iterated":[170],"computation":[171],"proving":[176],"iteration":[180],"gives":[185],"exactly":[186],"using":[191],"Maclaurin":[193],"polynomial":[194],"degree":[196],"k.":[197],"latter":[199],"result":[200],"paves":[201],"way":[203],"towards":[204],"application":[206],"methods":[209],"study":[212],"PageRank.":[214]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":10}],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}
