{"id":"https://openalex.org/W2002850151","doi":"https://doi.org/10.1137/040608635","title":"Graph Clustering Via a Discrete Uncoupling Process","display_name":"Graph Clustering Via a Discrete Uncoupling Process","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2002850151","doi":"https://doi.org/10.1137/040608635","mag":"2002850151"},"language":"en","primary_location":{"id":"doi:10.1137/040608635","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040608635","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5055403757","display_name":"Stijn van Dongen","orcid":"https://orcid.org/0000-0002-1487-1777"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stijn Van Dongen","raw_affiliation_strings":["svd@sanger.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"svd@sanger.ac.uk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055403757"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":16.3217,"has_fulltext":false,"cited_by_count":804,"citation_normalized_percentile":{"value":0.99478761,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"30","issue":"1","first_page":"121","last_page":"141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9990000128746033,"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":0.9990000128746033,"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/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9733999967575073,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9657999873161316,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.74143385887146},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.49104809761047363},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.48882123827934265},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.47084280848503113},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.462205171585083},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.45326563715934753},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4506242573261261},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4309671223163605},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.4248397946357727},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42377331852912903},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36885738372802734},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3541189134120941},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3425131142139435},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14361518621444702}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.74143385887146},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.49104809761047363},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.48882123827934265},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.47084280848503113},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.462205171585083},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.45326563715934753},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4506242573261261},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4309671223163605},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.4248397946357727},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42377331852912903},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36885738372802734},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3541189134120941},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3425131142139435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14361518621444702},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040608635","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040608635","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5799999833106995,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W11253727","https://openalex.org/W1488435683","https://openalex.org/W1510029899","https://openalex.org/W1514107797","https://openalex.org/W1520007244","https://openalex.org/W1568495775","https://openalex.org/W1582145286","https://openalex.org/W1982095877","https://openalex.org/W1984865036","https://openalex.org/W1993111701","https://openalex.org/W1999285709","https://openalex.org/W2004231585","https://openalex.org/W2006309149","https://openalex.org/W2008856488","https://openalex.org/W2009561564","https://openalex.org/W2014101418","https://openalex.org/W2020010559","https://openalex.org/W2021360000","https://openalex.org/W2028454531","https://openalex.org/W2035001157","https://openalex.org/W2037441094","https://openalex.org/W2042624802","https://openalex.org/W2047757567","https://openalex.org/W2052440141","https://openalex.org/W2062762227","https://openalex.org/W2074308942","https://openalex.org/W2082042541","https://openalex.org/W2090415636","https://openalex.org/W2094823810","https://openalex.org/W2096290331","https://openalex.org/W2096778187","https://openalex.org/W2100585269","https://openalex.org/W2111044742","https://openalex.org/W2114030927","https://openalex.org/W2115843776","https://openalex.org/W2118103211","https://openalex.org/W2121564430","https://openalex.org/W2124166542","https://openalex.org/W2126114820","https://openalex.org/W2131921202","https://openalex.org/W2137441463","https://openalex.org/W2166557397","https://openalex.org/W2610857016"],"related_works":["https://openalex.org/W2734729804","https://openalex.org/W2186430569","https://openalex.org/W3041997070","https://openalex.org/W1968612088","https://openalex.org/W2364963676","https://openalex.org/W2735388074","https://openalex.org/W2351194865","https://openalex.org/W4388292488","https://openalex.org/W2756643213","https://openalex.org/W1262344082"],"abstract_inverted_index":{"A":[0],"discrete":[1],"uncoupling":[2,360],"process":[3,19,34,119,146,158,183,224,230,241,321],"for":[4,23,151,272,286],"finite":[5],"spaces":[6],"is":[7,20,95,127,147,159,194,212,270,296,330,338,351],"introduced,":[8],"called":[9,28],"the":[10,15,21,24,29,56,63,83,104,118,139,145,163,174,182,209,222,229,238,250,292,312,318,332,339,344,352,359,363],"Markov":[11],"Cluster":[12],"Process":[13],"or":[14],"MCL":[16,30,33,210,223],"process.":[17],"The":[18,32,91,142,157,192,245,264,325],"engine":[22],"graph":[25,171,179],"clustering":[26,188],"algorithm":[27,211],"algorithm.":[31],"takes":[35],"a":[36,50,67,75,124,169,187,204,259,279,288,303,308],"stochastic":[37,51,68,87,289],"matrix":[38,52,131,164,261,305],"as":[39],"input,":[40],"and":[41,45,107,133,173,199,215,285,349],"then":[42],"alternates":[43],"expansion":[44],"inflation,":[46,134],"each":[47,99,109],"step":[48],"defining":[49],"in":[53,101,195,203],"terms":[54],"of":[55,66,85,165,177,190,221,252,315,320,327,331,341,343,354,362],"previous":[57],"one.":[58],"Expansion":[59],"corresponds":[60,73],"with":[61,74,135,347],"taking":[62],"kth":[64],"power":[65,106],"matrix,":[69,291],"where":[70,336],"$k\\in\\N$.":[71],"Inflation":[72],"parametrized":[76],"operator":[77,247],"$\\Gamma_r$,":[78],"$r\\geq":[79],"0$,":[80],"that":[81,126,208,254,274],"maps":[82,249],"set":[84],"(column)":[86],"matrices":[88,253,273],"onto":[89,243,262,323],"itself.":[90,263],"image":[92,293],"$\\Gamma_r":[93,294],"M$":[94,295,329],"obtained":[96],"by":[97,302],"raising":[98],"entry":[100],"M":[102,287,306],"to":[103,111,162,258,278,358],"rth":[105],"rescaling":[108],"column":[110],"have":[112],"sum":[113],"1":[114],"again.":[115],"In":[116],"practice":[117],"converges":[120],"very":[121,213],"fast":[122,214],"towards":[123],"limit":[125,140,184,193],"invariant":[128],"under":[129],"both":[130],"multiplication":[132],"quadratic":[136],"convergence":[137],"around":[138],"points.":[141],"heuristic":[143],"behind":[144],"its":[148],"expected":[149],"behavior":[150],"(Markov)":[152],"graphs":[153],"possessing":[154],"cluster":[155],"structure.":[156],"typically":[160],"applied":[161],"random":[166],"walks":[167],"on":[168],"given":[170],"G,":[172],"connected":[175],"components":[176],"(the":[178],"associated":[180,346],"with)":[181],"generically":[185],"allow":[186],"interpretation":[189],"G.":[191],"general":[196],"extremely":[197],"sparse":[198,202],"iterands":[200,233],"are":[201,225,255,275],"weighted":[205],"sense,":[206],"implying":[207],"highly":[216],"scalable.":[217],"Several":[218],"mathematical":[219],"properties":[220,236],"established.":[226],"Most":[227],"notably,":[228],"(and":[231],"algorithm)":[232],"posses":[234],"structural":[235],"generalizing":[237,317],"mapping":[239,319],"from":[240],"limits":[242,322],"clusterings.":[244,324],"inflation":[246,364],"$\\Gamma_r$":[248],"class":[251],"diagonally":[256,266,276],"similar":[257,277],"symmetric":[260],"phrase":[265],"positive":[267,280],"semi-definite":[268,281],"(dpsd)":[269],"used":[271],"matrix.":[282],"For":[283],"$r\\in\\N$":[284],"dpsd":[290,304],"again":[297],"dpsd.":[298],"Determinantal":[299],"inequalities":[300],"satisfied":[301],"imply":[307],"natural":[309],"ordering":[310,345],"among":[311],"diagonal":[313],"elements":[314],"M,":[316,348],"spectrum":[326],"$\\Gamma_{\\infty}":[328],"form":[333],"$\\{0^{n-k},":[334],"1^k\\}$,":[335],"k":[337],"number":[340],"endclasses":[342],"n":[350],"dimension":[353],"M.":[355],"This":[356],"attests":[357],"effect":[361],"operator.":[365]},"counts_by_year":[{"year":2026,"cited_by_count":59},{"year":2025,"cited_by_count":110},{"year":2024,"cited_by_count":144},{"year":2023,"cited_by_count":65},{"year":2022,"cited_by_count":34},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":31},{"year":2019,"cited_by_count":35},{"year":2018,"cited_by_count":40},{"year":2017,"cited_by_count":33},{"year":2016,"cited_by_count":44},{"year":2015,"cited_by_count":31},{"year":2014,"cited_by_count":37},{"year":2013,"cited_by_count":24},{"year":2012,"cited_by_count":36}],"updated_date":"2026-06-25T08:15:23.626066","created_date":"2025-10-10T00:00:00"}
