{"id":"https://openalex.org/W4200258318","doi":"https://doi.org/10.1109/tcyb.2021.3128361","title":"Topological Properties, Spectra Analysis, and Consensus Problems for a Class of Network Models Based on <i>m</i>-Fission Operation","display_name":"Topological Properties, Spectra Analysis, and Consensus Problems for a Class of Network Models Based on <i>m</i>-Fission Operation","publication_year":2021,"publication_date":"2021-12-15","ids":{"openalex":"https://openalex.org/W4200258318","doi":"https://doi.org/10.1109/tcyb.2021.3128361","pmid":"https://pubmed.ncbi.nlm.nih.gov/34910646"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2021.3128361","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3128361","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/A5101558941","display_name":"Zhizhuo Zhang","orcid":"https://orcid.org/0000-0003-0529-1962"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhizhuo Zhang","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028608923","display_name":"Bo Wu","orcid":"https://orcid.org/0000-0002-1487-7255"},"institutions":[{"id":"https://openalex.org/I137056471","display_name":"Nanjing University of Finance and Economics","ror":"https://ror.org/031y8am81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137056471"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Wu","raw_affiliation_strings":["School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, China","institution_ids":["https://openalex.org/I137056471"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101558941"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":0.1298,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.48132637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"52","issue":"9","first_page":"9905","last_page":"9921"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9994000196456909,"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":0.9994000196456909,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9959999918937683,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.994700014591217,"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/topology","display_name":"Topology (electrical circuits)","score":0.5982404351234436},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5390865206718445},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.518743097782135},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4975476562976837},{"id":"https://openalex.org/keywords/fission","display_name":"Fission","score":0.48526450991630554},{"id":"https://openalex.org/keywords/dynamic-network-analysis","display_name":"Dynamic network analysis","score":0.48286083340644836},{"id":"https://openalex.org/keywords/clustering-coefficient","display_name":"Clustering coefficient","score":0.47494199872016907},{"id":"https://openalex.org/keywords/network-model","display_name":"Network model","score":0.4394703507423401},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4119589328765869},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34582337737083435},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32984355092048645},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2329915165901184},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.18964990973472595},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13688647747039795}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5982404351234436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5390865206718445},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.518743097782135},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4975476562976837},{"id":"https://openalex.org/C12294094","wikidata":"https://www.wikidata.org/wiki/Q929080","display_name":"Fission","level":3,"score":0.48526450991630554},{"id":"https://openalex.org/C13540734","wikidata":"https://www.wikidata.org/wiki/Q5318996","display_name":"Dynamic network analysis","level":2,"score":0.48286083340644836},{"id":"https://openalex.org/C22047676","wikidata":"https://www.wikidata.org/wiki/Q898680","display_name":"Clustering coefficient","level":3,"score":0.47494199872016907},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.4394703507423401},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4119589328765869},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34582337737083435},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32984355092048645},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2329915165901184},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.18964990973472595},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13688647747039795},{"id":"https://openalex.org/C152568617","wikidata":"https://www.wikidata.org/wiki/Q2348","display_name":"Neutron","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2021.3128361","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2021.3128361","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:34910646","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34910646","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/G7623002341","display_name":null,"funder_award_id":"12026214","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W71943752","https://openalex.org/W1595344052","https://openalex.org/W1619246527","https://openalex.org/W1864806140","https://openalex.org/W1971421925","https://openalex.org/W1982424611","https://openalex.org/W1986269714","https://openalex.org/W2008620264","https://openalex.org/W2032121576","https://openalex.org/W2034810439","https://openalex.org/W2036039884","https://openalex.org/W2042479609","https://openalex.org/W2042916854","https://openalex.org/W2048572907","https://openalex.org/W2056598819","https://openalex.org/W2070722739","https://openalex.org/W2077856845","https://openalex.org/W2078206416","https://openalex.org/W2079006313","https://openalex.org/W2080478510","https://openalex.org/W2086016772","https://openalex.org/W2090463147","https://openalex.org/W2095293504","https://openalex.org/W2096836727","https://openalex.org/W2099689250","https://openalex.org/W2100240966","https://openalex.org/W2107362923","https://openalex.org/W2107396783","https://openalex.org/W2110620844","https://openalex.org/W2124451866","https://openalex.org/W2124620758","https://openalex.org/W2124637492","https://openalex.org/W2126927299","https://openalex.org/W2127048411","https://openalex.org/W2129004493","https://openalex.org/W2129107602","https://openalex.org/W2129248505","https://openalex.org/W2132734429","https://openalex.org/W2136931666","https://openalex.org/W2148606196","https://openalex.org/W2151685478","https://openalex.org/W2151936673","https://openalex.org/W2153624566","https://openalex.org/W2164727176","https://openalex.org/W2172813797","https://openalex.org/W2266296957","https://openalex.org/W2266714125","https://openalex.org/W2425329461","https://openalex.org/W2767159587","https://openalex.org/W2772804860","https://openalex.org/W2783384406","https://openalex.org/W2786933610","https://openalex.org/W2799047769","https://openalex.org/W2807511666","https://openalex.org/W2882985437","https://openalex.org/W2883160139","https://openalex.org/W2884141964","https://openalex.org/W2910561360","https://openalex.org/W2963287098","https://openalex.org/W2963308324","https://openalex.org/W3014271905","https://openalex.org/W3100106228","https://openalex.org/W3102505974","https://openalex.org/W3102641634","https://openalex.org/W3106442811","https://openalex.org/W3106753174","https://openalex.org/W4247782380","https://openalex.org/W4250134109"],"related_works":["https://openalex.org/W3099594505","https://openalex.org/W2909842655","https://openalex.org/W2064432722","https://openalex.org/W2357702059","https://openalex.org/W2392215070","https://openalex.org/W62337483","https://openalex.org/W2542000018","https://openalex.org/W2352811148","https://openalex.org/W3025826829","https://openalex.org/W2617506565"],"abstract_inverted_index":{"The":[0],"network":[1,5,9,60,95,107,118,141,146,193,236],"model,":[2],"especially":[3],"the":[4,36,44,50,80,86,91,100,103,106,113,117,138,155,162,165,170,172,176,183,187,190,198,203,207,212,216,219,223,231,235,239,244,248,252],"model":[6,96,237],"constructed":[7,41],"by":[8],"operation,":[10,71],"is":[11,40,53,109,142,180,194],"an":[12],"important":[13],"tool":[14],"to":[15,161,169,211,230,251],"study":[16],"complex":[17,25,57],"networks.":[18,58],"Many":[19,59],"topological":[20,81,114],"and":[21,82,90,99,127,150,182,222,238,262],"dynamic":[22,83,156,213],"properties":[23,84,115,157,214],"of":[24,46,85,102,116,164,175,186,189,206,225],"networks":[26],"can":[27,134],"be":[28,135],"studied":[29],"in":[30,49,56,178],"this":[31,34,70],"way.":[32],"In":[33],"article,":[35],"m":[37,87],"-fission":[38,88],"operation":[39,89,104,179],"based":[42,68],"on":[43,69,105,197,215,247],"phenomenon":[45],"node":[47],"splitting":[48],"network,":[51,171,217,253],"which":[52],"quite":[54],"common":[55],"models,":[61],"including":[62,218,254],"dual":[63],"Sierpinski":[64],"gaskets,":[65],"are":[66,97,158],"built":[67],"but":[72],"it":[73,133],"has":[74],"never":[75],"been":[76],"systematically":[77],"studied.":[78],"Then,":[79],"corresponding":[92,168,250],"iterative":[93,139,173,191],"fission":[94,140,192],"studied,":[98,181],"influence":[101],"structure":[108],"revealed.":[110],"Among":[111],"them,":[112],"include":[119],"diameter,":[120],"degree":[121],"distribution,":[122],"clustering":[123,149],"coefficient,":[124],"average":[125,224],"distance,":[126],"modularity.":[128],"By":[129],"studying":[130],"these":[131],"properties,":[132],"concluded":[136],"that":[137],"a":[143],"fractal":[144],"homogeneous":[145],"with":[147],"high":[148,151],"community":[152],"characteristics.":[153],"Since":[154],"closely":[159],"related":[160,210],"spectrum":[163,177,188],"Laplacian":[166],"matrix":[167],"relation":[174],"complete":[184],"solution":[185],"obtained.":[195],"Based":[196],"above":[199],"results,":[200],"we":[201,241],"calculate":[202],"analytical":[204],"expressions":[205],"characteristic":[208],"quantities":[209],"Kirchhoff":[220],"index":[221],"hitting":[226],"times.":[227],"Finally,":[228],"due":[229],"close":[232],"connection":[233],"between":[234],"system,":[240],"further":[242],"analyzed":[243],"consensus":[245],"problems":[246],"system":[249],"convergence":[255],"rate,":[256],"delay":[257],"robustness,":[258],"first-order":[259],"noise":[260,264],"coherence,":[261],"second-order":[263],"coherence.":[265]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-12-31T00:00:00"}
