{"id":"https://openalex.org/W1974709826","doi":"https://doi.org/10.1137/s1064827502412875","title":"Authority Rankings from HITS, PageRank, and SALSA: Existence, Uniqueness, and Effect of Initialization","display_name":"Authority Rankings from HITS, PageRank, and SALSA: Existence, Uniqueness, and Effect of Initialization","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1974709826","doi":"https://doi.org/10.1137/s1064827502412875","mag":"1974709826"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502412875","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502412875","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific 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/A5084212636","display_name":"Ayman Farahat","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ayman Farahat","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068789022","display_name":"Thomas LoFaro","orcid":"https://orcid.org/0000-0001-6711-8060"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas LoFaro","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102959104","display_name":"Joel C. Miller","orcid":"https://orcid.org/0000-0003-4426-0405"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joel C. Miller","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039676987","display_name":"Gregory Rae","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gregory Rae","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011205639","display_name":"Lesley A. Ward","orcid":"https://orcid.org/0000-0002-2226-7051"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lesley A. Ward","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5084212636"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.2656,"has_fulltext":false,"cited_by_count":119,"citation_normalized_percentile":{"value":0.97888002,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"27","issue":"4","first_page":"1181","last_page":"1201"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9991000294685364,"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":0.9991000294685364,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.992900013923645,"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/pagerank","display_name":"PageRank","score":0.9015619158744812},{"id":"https://openalex.org/keywords/hits-algorithm","display_name":"HITS algorithm","score":0.7460199594497681},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.6936956644058228},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6408669948577881},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6211609840393066},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5551130771636963},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5366363525390625},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4967799782752991},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.4576314091682434},{"id":"https://openalex.org/keywords/web-page","display_name":"Web page","score":0.44571423530578613},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3988291621208191},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.38350915908813477},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3803846538066864},{"id":"https://openalex.org/keywords/information-retrieval","display_name":"Information retrieval","score":0.26667553186416626},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.12090286612510681},{"id":"https://openalex.org/keywords/web-search-engine","display_name":"Web search engine","score":0.10715731978416443},{"id":"https://openalex.org/keywords/web-navigation","display_name":"Web navigation","score":0.0762987732887268}],"concepts":[{"id":"https://openalex.org/C2779172887","wikidata":"https://www.wikidata.org/wiki/Q184316","display_name":"PageRank","level":2,"score":0.9015619158744812},{"id":"https://openalex.org/C195409031","wikidata":"https://www.wikidata.org/wiki/Q1031957","display_name":"HITS algorithm","level":5,"score":0.7460199594497681},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6936956644058228},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6408669948577881},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6211609840393066},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5551130771636963},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5366363525390625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4967799782752991},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.4576314091682434},{"id":"https://openalex.org/C21959979","wikidata":"https://www.wikidata.org/wiki/Q36774","display_name":"Web page","level":2,"score":0.44571423530578613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3988291621208191},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38350915908813477},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3803846538066864},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.26667553186416626},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.12090286612510681},{"id":"https://openalex.org/C521815418","wikidata":"https://www.wikidata.org/wiki/Q4182287","display_name":"Web search engine","level":4,"score":0.10715731978416443},{"id":"https://openalex.org/C61096286","wikidata":"https://www.wikidata.org/wiki/Q7978592","display_name":"Web navigation","level":3,"score":0.0762987732887268},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1064827502412875","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502412875","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.7037","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.7037","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.hmc.edu/~ward/paperpdfs/hitsheaderbw6Jan05.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.99.3942","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.3942","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cnls.lanl.gov/~jomiller/publications/LinkUniqueness.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":22,"referenced_works":["https://openalex.org/W77115792","https://openalex.org/W199558496","https://openalex.org/W202534592","https://openalex.org/W391578156","https://openalex.org/W1490883626","https://openalex.org/W1854214752","https://openalex.org/W1968509530","https://openalex.org/W1977001629","https://openalex.org/W1990144193","https://openalex.org/W2006119904","https://openalex.org/W2020423193","https://openalex.org/W2026875114","https://openalex.org/W2043900215","https://openalex.org/W2066636486","https://openalex.org/W2079672501","https://openalex.org/W2089199911","https://openalex.org/W2138621811","https://openalex.org/W2141075029","https://openalex.org/W2610857016","https://openalex.org/W2798909945","https://openalex.org/W3108418035","https://openalex.org/W3139754459"],"related_works":["https://openalex.org/W3184283142","https://openalex.org/W2059631619","https://openalex.org/W1881353113","https://openalex.org/W2187771236","https://openalex.org/W2387616437","https://openalex.org/W2371803608","https://openalex.org/W2542162642","https://openalex.org/W1974709826","https://openalex.org/W2139394890","https://openalex.org/W1556894713"],"abstract_inverted_index":{"Algorithms":[0],"such":[1,172],"as":[2,50,84],"Kleinberg's":[3],"HITS":[4,131,160,182,200,208],"algorithm,":[5],"the":[6,14,22,38,48,70,74,79,85,98,101,105,111,114,118,121,130,142,145,148,159,177,180,194,199,215,243,248],"PageRank":[7,115],"algorithm":[8,16],"of":[9,17,25,28,64,73,81,100,113,120,144,155,176,179],"Brin":[10],"and":[11,13,19,77,108,117,132,161,230,250],"Page,":[12],"SALSA":[15,109,133,162,225,244],"Lempel":[18],"Moran":[20],"use":[21,78,89],"link":[23,71],"structure":[24,72],"a":[26,56,61,65,94,187,210,239],"network":[27,76,216],"web":[29],"pages":[30,49],"to":[31,34,46,92,123,164,191,193,198,207,234,242],"assign":[32],"weights":[33,41,252],"each":[35],"page":[36,86],"in":[37,174],"network.":[39],"The":[40],"can":[42,226],"then":[43],"be":[44,137],"used":[45],"rank":[47],"authoritative":[51],"sources.":[52],"These":[53],"algorithms":[54,122,146,163],"share":[55],"common":[57],"underpinning;":[58],"they":[59],"find":[60],"dominant":[62],"eigenvector":[63,83,103],"nonnegative":[66],"matrix":[67,196],"that":[68,129,157,204,214,224],"describes":[69],"given":[75],"entries":[80],"this":[82,90],"weights.":[87],"We":[88,139,152,169,185,202,236],"commonality":[91],"give":[93,153,227],"unified":[95],"treatment,":[96],"proving":[97],"existence":[99],"required":[102],"for":[104],"PageRank,":[106],"HITS,":[107,192],"algorithms,":[110],"uniqueness":[112],"eigenvector,":[116],"convergence":[119],"these":[124],"eigenvectors.":[125],"However,":[126],"we":[127],"show":[128,223],"eigenvectors":[134],"need":[135],"not":[136],"unique.":[138],"examine":[140],"how":[141],"initialization":[143,245],"affects":[147],"final":[149],"weightings":[150],"produced.":[151],"examples":[154,221],"networks":[156,173],"lead":[158],"returnnonunique":[165],"or":[166],"nonintuitive":[167],"rankings.":[168],"characterize":[170],"all":[171],"terms":[175],"connectivity":[178],"related":[181],"authority":[183,231,251],"graph.":[184],"propose":[186],"modification,":[188],"Exponentiated":[189,205],"Input":[190,206],"adjacency":[195],"input":[197],"algorithm.":[201],"prove":[203],"returns":[209],"unique":[211],"ranking,":[212],"provided":[213],"is":[217],"weakly":[218],"connected.":[219],"Our":[220],"also":[222,237],"inconsistent":[228],"hub":[229,249],"weights,":[232],"due":[233],"nonuniqueness.":[235],"mention":[238],"small":[240],"modification":[241],"which":[246],"makes":[247],"consistent.":[253]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":12}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}