{"id":"https://openalex.org/W2971451819","doi":"https://doi.org/10.1109/tcyb.2019.2933478","title":"Further Results for Edge Convergence of Directed Signed Networks","display_name":"Further Results for Edge Convergence of Directed Signed Networks","publication_year":2019,"publication_date":"2019-09-03","ids":{"openalex":"https://openalex.org/W2971451819","doi":"https://doi.org/10.1109/tcyb.2019.2933478","mag":"2971451819","pmid":"https://pubmed.ncbi.nlm.nih.gov/31484150"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2019.2933478","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2933478","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/A5022031952","display_name":"Mingjun Du","orcid":"https://orcid.org/0000-0003-1391-3936"},"institutions":[{"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":true,"raw_author_name":"Mingjun Du","raw_affiliation_strings":["School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China","Seventh Research Division, Beihang University (BUAA), Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Seventh Research Division, Beihang University (BUAA), Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103226195","display_name":"Baoli Ma","orcid":"https://orcid.org/0000-0002-9512-4852"},"institutions":[{"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":"Baoli Ma","raw_affiliation_strings":["School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China","Seventh Research Division, Beihang University (BUAA), Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Seventh Research Division, Beihang University (BUAA), Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038940032","display_name":"Deyuan Meng","orcid":"https://orcid.org/0000-0002-0990-0166"},"institutions":[{"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":"Deyuan Meng","raw_affiliation_strings":["School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China","Seventh Research Division, Beihang University (BUAA), Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Seventh Research Division, Beihang University (BUAA), Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022031952"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":1.4148,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83591004,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"51","issue":"12","first_page":"5659","last_page":"5670"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9987999796867371,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.995199978351593,"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/convergence","display_name":"Convergence (economics)","score":0.8321700692176819},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.6961451768875122},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6320191621780396},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.5679436326026917},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5199219584465027},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4644036293029785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.445008248090744},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.4444361925125122},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4115946590900421},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24475836753845215},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1953505575656891},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12168276309967041},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.05200773477554321}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.8321700692176819},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.6961451768875122},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6320191621780396},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.5679436326026917},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5199219584465027},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4644036293029785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.445008248090744},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.4444361925125122},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4115946590900421},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24475836753845215},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1953505575656891},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12168276309967041},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.05200773477554321},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"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":[{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2019.2933478","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2933478","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:31484150","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31484150","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":[],"awards":[{"id":"https://openalex.org/G1277797764","display_name":null,"funder_award_id":"YWF-19-BJ-J-42","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2398985662","display_name":null,"funder_award_id":"61573034","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5735234674","display_name":null,"funder_award_id":"61520106010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7305161236","display_name":null,"funder_award_id":"YWF-18-BJ-Y-25","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7424602539","display_name":null,"funder_award_id":"61922007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G890366264","display_name":null,"funder_award_id":"61873013","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/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W644218753","https://openalex.org/W836351843","https://openalex.org/W1488435683","https://openalex.org/W1967509640","https://openalex.org/W1998765575","https://openalex.org/W2014530074","https://openalex.org/W2016910787","https://openalex.org/W2049119205","https://openalex.org/W2071727953","https://openalex.org/W2098523806","https://openalex.org/W2107396783","https://openalex.org/W2129390569","https://openalex.org/W2129488612","https://openalex.org/W2193718162","https://openalex.org/W2206832235","https://openalex.org/W2214962116","https://openalex.org/W2314675936","https://openalex.org/W2336115929","https://openalex.org/W2343734929","https://openalex.org/W2345265966","https://openalex.org/W2402931367","https://openalex.org/W2465203691","https://openalex.org/W2493687459","https://openalex.org/W2516079600","https://openalex.org/W2529636467","https://openalex.org/W2530794077","https://openalex.org/W2562703567","https://openalex.org/W2586616317","https://openalex.org/W2588573379","https://openalex.org/W2592442839","https://openalex.org/W2737346335","https://openalex.org/W2765409557","https://openalex.org/W2766006709","https://openalex.org/W2769537296","https://openalex.org/W2786993706","https://openalex.org/W2797063385","https://openalex.org/W2883488044","https://openalex.org/W2890958849","https://openalex.org/W2891079296","https://openalex.org/W2899510315","https://openalex.org/W2905032080","https://openalex.org/W2911261112","https://openalex.org/W2918002354","https://openalex.org/W2921240485","https://openalex.org/W2922446740","https://openalex.org/W2963276546","https://openalex.org/W3101211700"],"related_works":["https://openalex.org/W2086397253","https://openalex.org/W2133122801","https://openalex.org/W2374925474","https://openalex.org/W600422426","https://openalex.org/W2007156430","https://openalex.org/W3081478936","https://openalex.org/W2972623885","https://openalex.org/W2073397884","https://openalex.org/W4389325756","https://openalex.org/W2785612136"],"abstract_inverted_index":{"The":[0,35,58,151],"edge":[1,47,85,111,163],"convergence":[2,48,146,164],"problems":[3,147],"have":[4],"been":[5],"explored":[6],"for":[7,60],"directed":[8],"signed":[9,74,100,149],"networks":[10],"recently":[11],"in":[12,38],"2019":[13],"by":[14],"Du,":[15],"Ma,":[16],"and":[17,43,106],"Meng,":[18],"of":[19,31,63,137,148,160],"which":[20],"the":[21,28,32,46,52,61,84,133,144,158,161],"analysis":[22],"results,":[23],"however,":[24],"depend":[25],"heavily":[26],"on":[27],"strong":[29,53],"connectivity":[30,54],"network":[33,75,101],"topologies.":[34],"question":[36],"asked":[37],"this":[39],"article":[40],"is:":[41],"whether":[42],"how":[44],"can":[45,87,139],"be":[49,88,140],"achieved":[50],"when":[51],"is":[55,66,69,76,102],"not":[56,114],"satisfied?":[57],"answer":[59],"case":[62],"spanning":[64],"tree":[65],"given.":[67],"It":[68],"shown":[70],"that":[71],"if":[72,98],"a":[73,93,99,117,124,129],"either":[77],"structurally":[78,104],"balanced":[79],"or":[80],"r-structurally":[81,107],"unbalanced,":[82],"then":[83,109],"state":[86,112],"ensured":[89],"to":[90,92,116,123,142,156],"converge":[91,115],"constant":[94,118,130],"vector.":[95],"In":[96],"contrast,":[97],"both":[103],"unbalanced":[105],"balanced,":[108],"its":[110],"does":[113],"vector":[119,126],"any":[120],"longer,":[121],"but":[122],"time-varying":[125],"trajectory":[127],"with":[128],"speed.":[131],"Further,":[132],"dynamic":[134],"behavior":[135],"results":[136],"edges":[138],"derived":[141],"address":[143],"node":[145],"networks.":[150],"simulation":[152],"examples":[153],"are":[154],"provided":[155],"illustrate":[157],"validity":[159],"established":[162],"results.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}