{"id":"https://openalex.org/W3000093441","doi":"https://doi.org/10.1109/tcsi.2019.2963687","title":"Optimizing Synchronizability of Multilayer Networks Based on the Graph Comparison Method","display_name":"Optimizing Synchronizability of Multilayer Networks Based on the Graph Comparison Method","publication_year":2020,"publication_date":"2020-01-14","ids":{"openalex":"https://openalex.org/W3000093441","doi":"https://doi.org/10.1109/tcsi.2019.2963687","mag":"3000093441"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2019.2963687","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2019.2963687","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","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/A5100387514","display_name":"Hui Liu","orcid":"https://orcid.org/0009-0006-7165-4257"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hui Liu","raw_affiliation_strings":["School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102032195","display_name":"Jiangqiao Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiangqiao Xu","raw_affiliation_strings":["School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109487251","display_name":"Zengyang Li","orcid":null},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zengyang Li","raw_affiliation_strings":["School of Computer Science, Central China Normal University, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100459915","display_name":"Xiaoping Wang","orcid":"https://orcid.org/0000-0002-4909-8286"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoping Wang","raw_affiliation_strings":["School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027725400","display_name":"Jinhu L\u00fc","orcid":"https://orcid.org/0000-0003-0275-8387"},"institutions":[{"id":"https://openalex.org/I4391767781","display_name":"State Key Laboratory of Software Development Environment","ror":"https://ror.org/017r4dj03","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767781","https://openalex.org/I82880672"]},{"id":"https://openalex.org/I4210165198","display_name":"Beijing Advanced Sciences and Innovation Center","ror":"https://ror.org/05qm21180","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165198"]},{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinhu Lu","raw_affiliation_strings":["Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China","State Key Laboratory of Software Development Environment, School of Automation Science and Electrical Engineering, Beihan University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I4210165198","https://openalex.org/I82880672"]},{"raw_affiliation_string":"State Key Laboratory of Software Development Environment, School of Automation Science and Electrical Engineering, Beihan University, Beijing, China","institution_ids":["https://openalex.org/I4391767781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081245089","display_name":"Zhigang Zeng","orcid":"https://orcid.org/0000-0003-4587-3588"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhigang Zeng","raw_affiliation_strings":["School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5100387514"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":1.7711,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85487087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"67","issue":"5","first_page":"1740","last_page":"1751"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9973000288009644,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/betweenness-centrality","display_name":"Betweenness centrality","score":0.8656350374221802},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.6358312368392944},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.6283866763114929},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5417305827140808},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5140677690505981},{"id":"https://openalex.org/keywords/centrality","display_name":"Centrality","score":0.48584672808647156},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.4767875671386719},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4288448393344879},{"id":"https://openalex.org/keywords/power-graph-analysis","display_name":"Power graph analysis","score":0.42421141266822815},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4070817828178406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3856889307498932},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.382305383682251},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3516397476196289},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14639145135879517},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09594693779945374}],"concepts":[{"id":"https://openalex.org/C117045392","wikidata":"https://www.wikidata.org/wiki/Q4899215","display_name":"Betweenness centrality","level":3,"score":0.8656350374221802},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.6358312368392944},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.6283866763114929},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5417305827140808},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5140677690505981},{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.48584672808647156},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.4767875671386719},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4288448393344879},{"id":"https://openalex.org/C106937863","wikidata":"https://www.wikidata.org/wiki/Q7236518","display_name":"Power graph analysis","level":3,"score":0.42421141266822815},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4070817828178406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3856889307498932},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.382305383682251},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3516397476196289},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14639145135879517},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09594693779945374},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2019.2963687","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2019.2963687","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3002100101","display_name":null,"funder_award_id":"61702377","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3523307272","display_name":null,"funder_award_id":"61621003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5353600475","display_name":null,"funder_award_id":"2017CFB426","funder_id":"https://openalex.org/F4320322186","funder_display_name":"Natural Science Foundation of Hubei Province"},{"id":"https://openalex.org/G7444543045","display_name":null,"funder_award_id":"2016YFB0800401","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G7462510006","display_name":null,"funder_award_id":"61876209","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7736959020","display_name":null,"funder_award_id":"61773175","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322186","display_name":"Natural Science Foundation of Hubei Province","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W607068030","https://openalex.org/W1968971635","https://openalex.org/W1971421925","https://openalex.org/W1980392184","https://openalex.org/W1994830523","https://openalex.org/W1996152536","https://openalex.org/W2002470750","https://openalex.org/W2012535317","https://openalex.org/W2014217492","https://openalex.org/W2030249432","https://openalex.org/W2034904095","https://openalex.org/W2045552397","https://openalex.org/W2045673922","https://openalex.org/W2050716737","https://openalex.org/W2050766178","https://openalex.org/W2063539292","https://openalex.org/W2079897686","https://openalex.org/W2085228033","https://openalex.org/W2097053956","https://openalex.org/W2098005762","https://openalex.org/W2117362627","https://openalex.org/W2148606196","https://openalex.org/W2153841181","https://openalex.org/W2159826786","https://openalex.org/W2160415132","https://openalex.org/W2167955841","https://openalex.org/W2168452204","https://openalex.org/W2169192458","https://openalex.org/W2283907552","https://openalex.org/W2285310709","https://openalex.org/W2294347342","https://openalex.org/W2386531825","https://openalex.org/W2494834885","https://openalex.org/W2521458040","https://openalex.org/W2547596511","https://openalex.org/W2767616979","https://openalex.org/W2783130794","https://openalex.org/W2795363994","https://openalex.org/W2798172508","https://openalex.org/W2899618753","https://openalex.org/W2913987530","https://openalex.org/W2963664619","https://openalex.org/W2964117853","https://openalex.org/W2965489695","https://openalex.org/W3103589660","https://openalex.org/W3111253645","https://openalex.org/W6750426845"],"related_works":["https://openalex.org/W1973509935","https://openalex.org/W2107855069","https://openalex.org/W2611574733","https://openalex.org/W2241641394","https://openalex.org/W2140653560","https://openalex.org/W2348831795","https://openalex.org/W4312461432","https://openalex.org/W2965490984","https://openalex.org/W3077030258","https://openalex.org/W1848393892"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,19,68,92],"aimed":[3],"at":[4],"optimizing":[5],"the":[6,13,35,39,47,54,75,108,136],"synchronizability":[7,37],"of":[8,15,41,46,56,89],"a":[9,30,65],"complex":[10,31,100],"network":[11,32],"when":[12],"total":[14],"its":[16],"edge":[17,27,81,140],"weights":[18,28,55,82],"given":[20],"and":[21,95,122,139],"fixed.":[22],"We":[23],"try":[24],"to":[25,33,61,86,105],"allocate":[26],"on":[29,50,118],"optimize":[34],"network's":[36],"from":[38],"perspective":[40],"spectral":[42],"graph":[43,76],"theory.":[44],"Most":[45],"existing":[48],"analysis":[49],"multilayer":[51],"networks":[52,121],"assumes":[53],"intralayer":[57],"or":[58],"interlayer":[59],"edges":[60],"be":[62],"identical.":[63],"Such":[64],"restrictive":[66],"assumption":[67],"not":[69],"made":[70],"in":[71,103],"this":[72],"work.":[73],"Using":[74],"comparison":[77],"based":[78],"method,":[79],"different":[80],"are":[83],"allocated":[84],"according":[85],"topological":[87],"features":[88],"networks,":[90],"which":[91],"more":[93],"reasonable":[94],"consistent":[96],"with":[97],"most":[98],"physical":[99],"networks.":[101,124],"Furthermore,":[102],"order":[104],"find":[106],"out":[107,115],"best":[109],"edge-weight":[110,132],"allocation":[111,133],"scheme,":[112],"we":[113],"carried":[114],"numerical":[116],"simulations":[117],"typical":[119],"duplex":[120],"real-world":[123],"The":[125],"simulation":[126],"results":[127],"show":[128],"that":[129],"our":[130],"proposed":[131],"schemes":[134],"outperform":[135],"average,":[137],"degree-based,":[138],"betweenness":[141],"centrality":[142],"allocations.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4}],"updated_date":"2026-03-03T08:47:05.690250","created_date":"2025-10-10T00:00:00"}