{"id":"https://openalex.org/W7161696244","doi":"https://doi.org/10.3390/systems14050565","title":"Node Importance Evaluation Method Based on Fractional-Order Topological Propagation and Local Information Entropy","display_name":"Node Importance Evaluation Method Based on Fractional-Order Topological Propagation and Local Information Entropy","publication_year":2026,"publication_date":"2026-05-15","ids":{"openalex":"https://openalex.org/W7161696244","doi":"https://doi.org/10.3390/systems14050565"},"language":"en","primary_location":{"id":"doi:10.3390/systems14050565","is_oa":true,"landing_page_url":"https://doi.org/10.3390/systems14050565","pdf_url":null,"source":{"id":"https://openalex.org/S4210219410","display_name":"Systems","issn_l":"2079-8954","issn":["2079-8954"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/systems14050565","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040477073","display_name":"Kangzheng Huang","orcid":"https://orcid.org/0000-0002-1457-9872"},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kangzheng Huang","raw_affiliation_strings":["School of Automation, Wuhan University of Technology, Wuhan 430070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation, Wuhan University of Technology, Wuhan 430070, China","institution_ids":["https://openalex.org/I196699116"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100371213","display_name":"Weiwei Li","orcid":"https://orcid.org/0000-0002-7329-4236"},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]},{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weibo Li","raw_affiliation_strings":["College of Electrical Engineering, Northwest Minzu University, Lanzhou 730124, China","School of Automation, Wuhan University of Technology, Wuhan 430070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Electrical Engineering, Northwest Minzu University, Lanzhou 730124, China","institution_ids":["https://openalex.org/I145897649"]},{"raw_affiliation_string":"School of Automation, Wuhan University of Technology, Wuhan 430070, China","institution_ids":["https://openalex.org/I196699116"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041883250","display_name":"Shuai Cao","orcid":"https://orcid.org/0000-0002-5562-721X"},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuai Cao","raw_affiliation_strings":["School of Automation, Wuhan University of Technology, Wuhan 430070, China"],"raw_orcid":"https://orcid.org/0009-0002-5663-8858","affiliations":[{"raw_affiliation_string":"School of Automation, Wuhan University of Technology, Wuhan 430070, China","institution_ids":["https://openalex.org/I196699116"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042338108","display_name":"Xianping Zhu","orcid":"https://orcid.org/0000-0002-7611-5512"},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianping Zhu","raw_affiliation_strings":["School of Automation, Wuhan University of Technology, Wuhan 430070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation, Wuhan University of Technology, Wuhan 430070, China","institution_ids":["https://openalex.org/I196699116"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5136473888","display_name":"Peng Li","orcid":null},"institutions":[{"id":"https://openalex.org/I4210129465","display_name":"Wuhan Ship Development & Design Institute","ror":"https://ror.org/02mcdae06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210129465"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng Li","raw_affiliation_strings":["Wuhan Second Ship Design and Research Institute, Wuhan 430205, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wuhan Second Ship Design and Research Institute, Wuhan 430205, China","institution_ids":["https://openalex.org/I4210129465"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.60952653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"5","first_page":"565","last_page":"565"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.6916999816894531,"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":0.6916999816894531,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.13089999556541443,"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/T11476","display_name":"Graph theory and applications","score":0.041099999099969864,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/centrality","display_name":"Centrality","score":0.586899995803833},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.48919999599456787},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.41940000653266907},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.41100001335144043},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.40950000286102295},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.39809998869895935},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.39739999175071716},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.3968999981880188},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.3894999921321869}],"concepts":[{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.586899995803833},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.48919999599456787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45890000462532043},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.41940000653266907},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.41100001335144043},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40950000286102295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4081000089645386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4074999988079071},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39739999175071716},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3968999981880188},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.3894999921321869},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.32190001010894775},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.31929999589920044},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.31130000948905945},{"id":"https://openalex.org/C137753397","wikidata":"https://www.wikidata.org/wiki/Q2434424","display_name":"Network science","level":3,"score":0.3075999915599823},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C117045392","wikidata":"https://www.wikidata.org/wiki/Q4899215","display_name":"Betweenness centrality","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.28380000591278076},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C176032523","wikidata":"https://www.wikidata.org/wiki/Q753127","display_name":"Topological sorting","level":3,"score":0.27140000462532043},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.26930001378059387},{"id":"https://openalex.org/C167981619","wikidata":"https://www.wikidata.org/wiki/Q1685498","display_name":"Cross entropy","level":3,"score":0.2581999897956848},{"id":"https://openalex.org/C182049051","wikidata":"https://www.wikidata.org/wiki/Q17147155","display_name":"Transfer entropy","level":3,"score":0.2581000030040741},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/systems14050565","is_oa":true,"landing_page_url":"https://doi.org/10.3390/systems14050565","pdf_url":null,"source":{"id":"https://openalex.org/S4210219410","display_name":"Systems","issn_l":"2079-8954","issn":["2079-8954"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3c8ab74eb2ea40768025e7097c6a4d5a","is_oa":true,"landing_page_url":"https://doaj.org/article/3c8ab74eb2ea40768025e7097c6a4d5a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Systems, Vol 14, Iss 5, p 565 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/systems14050565","is_oa":true,"landing_page_url":"https://doi.org/10.3390/systems14050565","pdf_url":null,"source":{"id":"https://openalex.org/S4210219410","display_name":"Systems","issn_l":"2079-8954","issn":["2079-8954"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2012223088","display_name":null,"funder_award_id":"104972025YJS0119","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3010783864","display_name":null,"funder_award_id":"2024BAB067","funder_id":"https://openalex.org/F4320330031","funder_display_name":"Science and Technology Department of Hubei Province"}],"funders":[{"id":"https://openalex.org/F4320330031","display_name":"Science and Technology Department of Hubei Province","ror":null},{"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":33,"referenced_works":["https://openalex.org/W3088935735","https://openalex.org/W3210378911","https://openalex.org/W4212873627","https://openalex.org/W4283277456","https://openalex.org/W4290830324","https://openalex.org/W4309918968","https://openalex.org/W4320725525","https://openalex.org/W4380998086","https://openalex.org/W4384007550","https://openalex.org/W4385348942","https://openalex.org/W4390471111","https://openalex.org/W4390971793","https://openalex.org/W4399915662","https://openalex.org/W4400573382","https://openalex.org/W4402400949","https://openalex.org/W4405083197","https://openalex.org/W4406731406","https://openalex.org/W4407739288","https://openalex.org/W4411171727","https://openalex.org/W4412449682","https://openalex.org/W4412820398","https://openalex.org/W4413035164","https://openalex.org/W4413308736","https://openalex.org/W4413739252","https://openalex.org/W4413773366","https://openalex.org/W4414781913","https://openalex.org/W4415933720","https://openalex.org/W4415983373","https://openalex.org/W4416167072","https://openalex.org/W7119522298","https://openalex.org/W7131401076","https://openalex.org/W7143436443","https://openalex.org/W7151597905"],"related_works":[],"abstract_inverted_index":{"Accurate":[0],"identification":[1],"of":[2,27,35,74,102,129,168,233,250],"key":[3],"nodes":[4,263],"in":[5,79,200,264],"complex":[6],"networks":[7,164],"is":[8,122,143,228],"vital":[9],"for":[10],"optimizing":[11],"system":[12],"robustness":[13],"and":[14,64,165,186,195,207],"controlling":[15],"information":[16,66,119,132,141,154],"spread.":[17],"Existing":[18],"centrality":[19],"metrics":[20],"struggle":[21],"to":[22,124,146,237],"balance":[23],"the":[24,32,72,92,99,107,126,148,176,202,217,221,248,251,258,265],"continuous":[25,86],"extraction":[26],"global":[28,108,114,208],"topological":[29,62,88,109,267],"features":[30,105],"with":[31],"fine-grained":[33],"perception":[34],"local":[36,65,136,139],"structures,":[37],"while":[38],"traditional":[39,80],"heuristic":[40],"algorithms":[41,183],"also":[42,215],"face":[43],"severe":[44],"resolution":[45],"limitations.":[46],"To":[47],"address":[48],"these":[49],"issues,":[50],"this":[51],"paper":[52],"proposes":[53],"a":[54,85,130],"node":[55,103],"importance":[56],"evaluation":[57],"method":[58,70,214],"based":[59],"on":[60,161],"fractional-order":[61,87],"propagation":[63,77,89],"entropy":[67,142],"(FSEC).":[68],"This":[69,97,254],"overcomes":[71],"limitations":[73],"discrete":[75],"integer-order":[76],"inherent":[78],"graph":[81,94],"walks.":[82],"It":[83],"constructs":[84],"operator":[90],"within":[91,134],"spectral":[93],"theory":[95,120],"framework.":[96],"enables":[98],"smooth":[100],"projection":[101],"degree":[104],"into":[106],"space,":[110],"thereby":[111],"yielding":[112],"high-order":[113],"impact":[115],"factors.":[116],"Furthermore,":[117],"an":[118],"mechanism":[121],"introduced":[123],"quantify":[125],"probability":[127],"distribution":[128],"node\u2019s":[131,149],"contribution":[133],"its":[135],"neighborhood.":[137],"The":[138,172,212],"structural":[140],"then":[144],"calculated":[145],"reflect":[147],"asymmetric":[150],"control":[151],"over":[152],"micro-level":[153],"flow.":[155],"Deliberate":[156],"attack":[157],"simulations":[158,245],"were":[159],"conducted":[160],"nine":[162],"real-world":[163],"three":[166],"types":[167],"artificial":[169],"network":[170,209],"models.":[171],"results":[173],"show":[174],"that":[175,232],"proposed":[177,213],"FSEC":[178,252],"algorithm":[179],"significantly":[180],"outperforms":[181],"baseline":[182,240],"like":[184],"Autoencoder":[185],"Graph":[187],"Neural":[188],"Network":[189],"(AGNN),":[190],"Degree":[191,197],"Centrality,":[192],"k-shell,":[193],"PageRank,":[194],"Mixed":[196],"Decomposition":[198],"(MDD)":[199],"degrading":[201],"largest":[203],"connected":[204],"component":[205],"(LCC)":[206],"efficiency":[210],"(NE).":[211],"achieves":[216],"minimum":[218],"Area":[219],"Under":[220],"Curve":[222],"(AUC)":[223],"values":[224],"globally.":[225],"Its":[226],"monotonicity":[227],"slightly":[229],"lower":[230],"than":[231],"AGNN":[234],"but":[235],"superior":[236],"all":[238],"other":[239],"algorithms.":[241],"In":[242],"addition,":[243],"SIR":[244],"further":[246],"confirm":[247],"effectiveness":[249],"method.":[253],"approach":[255],"successfully":[256],"resolves":[257],"ranking":[259],"tie":[260],"problem":[261],"among":[262],"same":[266],"layer.":[268]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-05-20T00:00:00"}
