{"id":"https://openalex.org/W2963827361","doi":"https://doi.org/10.1109/tcyb.2018.2868124","title":"Scale-Free Loopy Structure is Resistant to Noise in Consensus Dynamics in Complex Networks","display_name":"Scale-Free Loopy Structure is Resistant to Noise in Consensus Dynamics in Complex Networks","publication_year":2018,"publication_date":"2018-10-09","ids":{"openalex":"https://openalex.org/W2963827361","doi":"https://doi.org/10.1109/tcyb.2018.2868124","mag":"2963827361","pmid":"https://pubmed.ncbi.nlm.nih.gov/30273162"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2018.2868124","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2018.2868124","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5062353872","display_name":"Yuhao Yi","orcid":"https://orcid.org/0000-0001-6036-0276"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuhao Yi","raw_affiliation_strings":["Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067533846","display_name":"Zhongzhi Zhang","orcid":"https://orcid.org/0000-0003-1260-2079"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongzhi Zhang","raw_affiliation_strings":["Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-1260-2079","affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081738999","display_name":"Stacy Patterson","orcid":"https://orcid.org/0000-0001-7711-6018"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stacy Patterson","raw_affiliation_strings":["Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA"],"raw_orcid":"https://orcid.org/0000-0001-7711-6018","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2298,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.92807319,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"50","issue":"1","first_page":"190","last_page":"200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9988999962806702,"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":0.9988999962806702,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9979000091552734,"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/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.6223223805427551},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5405799746513367},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.503926694393158},{"id":"https://openalex.org/keywords/scale-free-network","display_name":"Scale-free network","score":0.47517648339271545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4364880919456482},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.3866560459136963},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3255213797092438},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.20907294750213623},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16966691613197327},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15739822387695312},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.14578214287757874},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.12219202518463135},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.09416550397872925}],"concepts":[{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.6223223805427551},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5405799746513367},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.503926694393158},{"id":"https://openalex.org/C25580894","wikidata":"https://www.wikidata.org/wiki/Q1071058","display_name":"Scale-free network","level":3,"score":0.47517648339271545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4364880919456482},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.3866560459136963},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3255213797092438},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.20907294750213623},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16966691613197327},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15739822387695312},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.14578214287757874},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.12219202518463135},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.09416550397872925},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2018.2868124","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2018.2868124","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:30273162","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30273162","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7900000214576721}],"awards":[{"id":"https://openalex.org/G3701836525","display_name":null,"funder_award_id":"CNS-1553340","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G537946182","display_name":null,"funder_award_id":"61872093","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6466356579","display_name":null,"funder_award_id":"CNS-1527287","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":80,"referenced_works":["https://openalex.org/W131619556","https://openalex.org/W1269932635","https://openalex.org/W1547358136","https://openalex.org/W1868559974","https://openalex.org/W1875795917","https://openalex.org/W1877916171","https://openalex.org/W1878853999","https://openalex.org/W1907790026","https://openalex.org/W1963658112","https://openalex.org/W1971537656","https://openalex.org/W1985451401","https://openalex.org/W1992195122","https://openalex.org/W1996409316","https://openalex.org/W1998200279","https://openalex.org/W2008620264","https://openalex.org/W2012445782","https://openalex.org/W2019334962","https://openalex.org/W2021761546","https://openalex.org/W2026337277","https://openalex.org/W2029940092","https://openalex.org/W2037322878","https://openalex.org/W2042890145","https://openalex.org/W2054114108","https://openalex.org/W2059412266","https://openalex.org/W2065313971","https://openalex.org/W2069519093","https://openalex.org/W2076451073","https://openalex.org/W2078620895","https://openalex.org/W2080478510","https://openalex.org/W2081084405","https://openalex.org/W2081723824","https://openalex.org/W2083951382","https://openalex.org/W2086016772","https://openalex.org/W2087427091","https://openalex.org/W2088012076","https://openalex.org/W2090247235","https://openalex.org/W2099689250","https://openalex.org/W2105850748","https://openalex.org/W2107396783","https://openalex.org/W2112090702","https://openalex.org/W2112147870","https://openalex.org/W2124451866","https://openalex.org/W2128018982","https://openalex.org/W2128448454","https://openalex.org/W2129248505","https://openalex.org/W2132734429","https://openalex.org/W2138624490","https://openalex.org/W2140488329","https://openalex.org/W2144267444","https://openalex.org/W2146890818","https://openalex.org/W2148606196","https://openalex.org/W2150973821","https://openalex.org/W2151685478","https://openalex.org/W2160643434","https://openalex.org/W2161984370","https://openalex.org/W2166417226","https://openalex.org/W2168515859","https://openalex.org/W2169475202","https://openalex.org/W2192950346","https://openalex.org/W2216737681","https://openalex.org/W2345718780","https://openalex.org/W2346565973","https://openalex.org/W2425329461","https://openalex.org/W2595972220","https://openalex.org/W2618208446","https://openalex.org/W2752776682","https://openalex.org/W2755628595","https://openalex.org/W2947171186","https://openalex.org/W2962921922","https://openalex.org/W2963204084","https://openalex.org/W2963995521","https://openalex.org/W3104175967","https://openalex.org/W3106163143","https://openalex.org/W3106753174","https://openalex.org/W4205987271","https://openalex.org/W4233647833","https://openalex.org/W4247782380","https://openalex.org/W6639440540","https://openalex.org/W6687614507","https://openalex.org/W7061399666"],"related_works":["https://openalex.org/W2955169294","https://openalex.org/W2944759572","https://openalex.org/W2088554646","https://openalex.org/W2373100292","https://openalex.org/W3125380556","https://openalex.org/W2316807176","https://openalex.org/W3009528591","https://openalex.org/W2085207701","https://openalex.org/W1992102981","https://openalex.org/W2381095075"],"abstract_inverted_index":{"The":[0],"vast":[1],"majority":[2],"of":[3,45,50,73,75,80,87,96,112,135,146,168],"real-world":[4,100],"networks":[5,46,114,128,151,176],"are":[6,35],"scale-free,":[7],"loopy,":[8],"and":[9,16,115,137,152],"sparse,":[10,98],"with":[11,185,194],"a":[12,17,70,76,104,124],"power-law":[13,175,201],"degree":[14],"distribution":[15],"constant":[18,125],"average":[19,82],"degree.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24,141],"study":[25,93,108,142],"first-order":[26],"consensus":[27,65,172,198],"dynamics":[28,173,199],"in":[29,48,78,174,200],"binary":[30],"scale-free":[31,99,182],"networks,":[32,101,119],"where":[33],"vertices":[34],"subject":[36],"to":[37,123,159,196],"white":[38],"noise.":[39],"We":[40,67,91,106,179],"focus":[41],"on":[42,132,170],"the":[43,51,61,64,88,94,110,127,133,138,144,154,166,171,191],"coherence":[44,74,95,111,136,145],"characterized":[47],"terms":[49,79],"H":[52],"<sub":[53],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[54],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[55],"-norm,":[56],"which":[57,84,102,120,157],"quantifies":[58],"how":[59],"closely":[60],"agents":[62],"track":[63],"value.":[66],"first":[68],"provide":[69],"lower":[71],"bound":[72],"network":[77,89],"its":[81],"degree,":[83],"is":[85,177,188],"independent":[86],"order.":[90],"then":[92],"some":[97],"approaches":[103],"constant.":[105],"also":[107,121],"numerically":[109],"Barab\u00e1si-Albert":[113],"high-dimensional":[116],"random":[117],"Apollonian":[118],"converges":[122],"when":[126],"grow.":[129],"Finally,":[130],"based":[131],"connection":[134],"Kirchhoff":[139],"index,":[140],"analytically":[143],"two":[147],"deterministically":[148],"growing":[149],"sparse":[150],"obtain":[153],"exact":[155],"expressions,":[156],"tend":[158],"small":[160],"constants.":[161],"Our":[162],"results":[163],"indicate":[164],"that":[165,181],"effect":[167],"noise":[169],"negligible.":[178],"argue":[180],"topology,":[183],"together":[184],"loopy":[186],"structure,":[187],"responsible":[189],"for":[190],"strong":[192],"robustness":[193],"respect":[195],"noisy":[197],"networks.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}