{"id":"https://openalex.org/W2807656928","doi":"https://doi.org/10.1109/tnse.2018.2884235","title":"Centrality Measures for Graphons: Accounting for Uncertainty in Networks","display_name":"Centrality Measures for Graphons: Accounting for Uncertainty in Networks","publication_year":2018,"publication_date":"2018-11-30","ids":{"openalex":"https://openalex.org/W2807656928","doi":"https://doi.org/10.1109/tnse.2018.2884235","mag":"2807656928"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2018.2884235","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2018.2884235","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1707.09350","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Marco Avella-Medina","orcid":"https://orcid.org/0000-0003-0248-2018"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marco Avella-Medina","raw_affiliation_strings":["Department of Statistics, Columbia University, New York, USA"],"raw_orcid":"https://orcid.org/0000-0003-0248-2018","affiliations":[{"raw_affiliation_string":"Department of Statistics, Columbia University, New York, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Francesca Parise","orcid":"https://orcid.org/0000-0003-0650-4392"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Francesca Parise","raw_affiliation_strings":["Laboratory for Information and Decision Systems, MIT, Cambridge, USA"],"raw_orcid":"https://orcid.org/0000-0003-0650-4392","affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, MIT, Cambridge, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Michael T. Schaub","orcid":"https://orcid.org/0000-0003-2426-6404"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210137115","display_name":"Data & Society Research Institute","ror":"https://ror.org/04dse4f93","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210137115"]},{"id":"https://openalex.org/I4210146410","display_name":"Science Oxford","ror":"https://ror.org/04j8yhy50","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210146410"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Michael T. Schaub","raw_affiliation_strings":["Department of Engineering Science, University of Oxford, Oxford, United Kingdom","Institute for Data, Systems, and Society, MIT, Cambridge, USA"],"raw_orcid":"https://orcid.org/0000-0003-2426-6404","affiliations":[{"raw_affiliation_string":"Department of Engineering Science, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210146410"]},{"raw_affiliation_string":"Institute for Data, Systems, and Society, MIT, Cambridge, USA","institution_ids":["https://openalex.org/I4210137115"]}]},{"author_position":"last","author":{"id":null,"display_name":"Santiago Segarra","orcid":"https://orcid.org/0000-0002-8408-9633"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Santiago Segarra","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rice University, Houston, USA"],"raw_orcid":"https://orcid.org/0000-0002-8408-9633","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, USA","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8526,"has_fulltext":true,"cited_by_count":63,"citation_normalized_percentile":{"value":0.95839663,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"7","issue":"1","first_page":"520","last_page":"537"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.4544999897480011,"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"}},"topics":[{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.4544999897480011,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.38260000944137573,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.04540000110864639,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/centrality","display_name":"Centrality","score":0.9851999878883362},{"id":"https://openalex.org/keywords/pagerank","display_name":"PageRank","score":0.7354999780654907},{"id":"https://openalex.org/keywords/premise","display_name":"Premise","score":0.6963000297546387},{"id":"https://openalex.org/keywords/katz-centrality","display_name":"Katz centrality","score":0.5893999934196472},{"id":"https://openalex.org/keywords/network-theory","display_name":"Network theory","score":0.5146999955177307},{"id":"https://openalex.org/keywords/network-science","display_name":"Network science","score":0.5145000219345093},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47130000591278076}],"concepts":[{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.9851999878883362},{"id":"https://openalex.org/C2779172887","wikidata":"https://www.wikidata.org/wiki/Q184316","display_name":"PageRank","level":2,"score":0.7354999780654907},{"id":"https://openalex.org/C2778023277","wikidata":"https://www.wikidata.org/wiki/Q321703","display_name":"Premise","level":2,"score":0.6963000297546387},{"id":"https://openalex.org/C131349576","wikidata":"https://www.wikidata.org/wiki/Q6378571","display_name":"Katz centrality","level":4,"score":0.5893999934196472},{"id":"https://openalex.org/C11804174","wikidata":"https://www.wikidata.org/wiki/Q1192971","display_name":"Network theory","level":2,"score":0.5146999955177307},{"id":"https://openalex.org/C137753397","wikidata":"https://www.wikidata.org/wiki/Q2434424","display_name":"Network science","level":3,"score":0.5145000219345093},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5084999799728394},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47130000591278076},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4683000147342682},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41029998660087585},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.40610000491142273},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3391999900341034},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C41982775","wikidata":"https://www.wikidata.org/wiki/Q7000977","display_name":"Network controllability","level":4,"score":0.2937000095844269},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnse.2018.2884235","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2018.2884235","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1707.09350","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1707.09350","pdf_url":"https://arxiv.org/pdf/1707.09350","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1707.09350","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1707.09350","pdf_url":"https://arxiv.org/pdf/1707.09350","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3390984437","display_name":null,"funder_award_id":"P2EGP1_168962","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G6365799935","display_name":null,"funder_award_id":"P300P2_177805","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G757996282","display_name":null,"funder_award_id":"P300P1_177746","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G766637375","display_name":null,"funder_award_id":"P2EZP2_168812","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2807656928.pdf","grobid_xml":"https://content.openalex.org/works/W2807656928.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W123186044","https://openalex.org/W273178449","https://openalex.org/W1536930209","https://openalex.org/W1555674425","https://openalex.org/W1830307536","https://openalex.org/W1848620603","https://openalex.org/W1883408324","https://openalex.org/W1971937094","https://openalex.org/W1980573399","https://openalex.org/W1985009003","https://openalex.org/W1985718595","https://openalex.org/W1988183975","https://openalex.org/W2013419997","https://openalex.org/W2018415308","https://openalex.org/W2032005951","https://openalex.org/W2038949443","https://openalex.org/W2042901984","https://openalex.org/W2053507997","https://openalex.org/W2056944867","https://openalex.org/W2061820396","https://openalex.org/W2064274783","https://openalex.org/W2082734581","https://openalex.org/W2087194317","https://openalex.org/W2088783191","https://openalex.org/W2102907934","https://openalex.org/W2111754130","https://openalex.org/W2114244473","https://openalex.org/W2115076673","https://openalex.org/W2119075126","https://openalex.org/W2121470019","https://openalex.org/W2127405101","https://openalex.org/W2130682975","https://openalex.org/W2137365113","https://openalex.org/W2138621811","https://openalex.org/W2233466420","https://openalex.org/W2304449369","https://openalex.org/W2570065583","https://openalex.org/W2622487651","https://openalex.org/W2766459737","https://openalex.org/W2784072063","https://openalex.org/W2784590133","https://openalex.org/W2962719258","https://openalex.org/W2962962954","https://openalex.org/W2963319455","https://openalex.org/W2964164193","https://openalex.org/W6604673409","https://openalex.org/W6630644091","https://openalex.org/W6631953675","https://openalex.org/W6638161325","https://openalex.org/W6639055396","https://openalex.org/W6641081013","https://openalex.org/W6674413621","https://openalex.org/W6678224435","https://openalex.org/W6687532740","https://openalex.org/W6693647824","https://openalex.org/W6744894902"],"related_works":[],"abstract_inverted_index":{"As":[0],"relational":[1],"datasets":[2],"modeled":[3],"as":[4,155],"graphs":[5,164],"keep":[6],"increasing":[7,166],"in":[8,63],"size":[9],"and":[10,23,90,138,144,181],"their":[11,92,158],"data-acquisition":[12],"is":[13,38,105],"permeated":[14],"by":[15],"uncertainty,":[16],"graph-based":[17],"analysis":[18],"techniques":[19],"can":[20],"become":[21],"computationally":[22],"conceptually":[24],"challenging.":[25],"In":[26],"particular,":[27],"node":[28],"centrality":[29,52,86,97,107,140,151,179,183,198],"measures":[30,53,87,108,184],"rely":[31],"on":[32,78,161,185],"the":[33,36,59,64,111,127,177,182,196],"assumption":[34],"that":[35,106,149],"graph":[37,96,124],"perfectly":[39],"known":[40],"-":[41],"a":[42,74,191],"premise":[43],"not":[44],"necessarily":[45],"fulfilled":[46],"for":[47,88,142],"large,":[48],"uncertain":[49],"networks.":[50],"Accordingly,":[51],"may":[54],"fail":[55],"to":[56,94,119],"faithfully":[57],"extract":[58],"importance":[60],"of":[61,66,85,102,114,122,129,157,163,165,193,195],"nodes":[62],"presence":[65],"uncertainty.":[67],"To":[68],"mitigate":[69],"these":[70],"problems,":[71],"we":[72,81,133],"suggest":[73],"statistical":[75],"approach":[76,104],"based":[77],"graphon":[79,150,178],"theory:":[80],"introduce":[82],"formal":[83],"definitions":[84],"graphons":[89,115,143],"establish":[91,145],"connections":[93],"classical":[95],"measures.":[98],"A":[99],"key":[100],"advantage":[101],"this":[103],"defined":[109,160],"at":[110],"modeling":[112],"level":[113],"are":[116],"inherently":[117],"robust":[118],"stochastic":[120],"variations":[121],"specific":[123],"realizations.":[125],"Using":[126],"theory":[128],"linear":[130],"integral":[131],"operators,":[132],"define":[134],"degree,":[135],"eigenvector,":[136],"Katz":[137],"PageRank":[139],"functions":[141,152,180],"concentration":[146,170],"inequalities":[147,171],"demonstrating":[148],"arise":[153],"naturally":[154],"limits":[156],"counterparts":[159],"sequences":[162],"size.":[167],"The":[168],"same":[169],"also":[172],"provide":[173],"high-probability":[174],"bounds":[175],"between":[176],"any":[186],"sampled":[187],"graph,":[188],"thereby":[189],"establishing":[190],"measure":[192],"uncertainty":[194],"measured":[197],"score.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2018-06-13T00:00:00"}