{"id":"https://openalex.org/W4391882807","doi":"https://doi.org/10.3390/sym16020243","title":"On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters","display_name":"On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters","publication_year":2024,"publication_date":"2024-02-16","ids":{"openalex":"https://openalex.org/W4391882807","doi":"https://doi.org/10.3390/sym16020243"},"language":"en","primary_location":{"id":"doi:10.3390/sym16020243","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020243","pdf_url":"https://www.mdpi.com/2073-8994/16/2/243/pdf?version=1708076967","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/2/243/pdf?version=1708076967","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035603374","display_name":"Da Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210111575","display_name":"Xinjiang Institute of Engineering","ror":"https://ror.org/01s5hh873","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210111575","https://openalex.org/I4210157944"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Da Huang","raw_affiliation_strings":["School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China","institution_ids":["https://openalex.org/I4210111575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112407290","display_name":"Jibin Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210103745","display_name":"Changji University","ror":"https://ror.org/016j41127","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210103745"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jibin Yang","raw_affiliation_strings":["School of Mathematics and Data Science, Changji University, Changji 831100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Data Science, Changji University, Changji 831100, China","institution_ids":["https://openalex.org/I4210103745"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075953124","display_name":"Zhiyong Yu","orcid":"https://orcid.org/0000-0001-8073-057X"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiyong Yu","raw_affiliation_strings":["School of Mathematics and System Science, Xinjiang University, Urumqi 830017, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and System Science, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071803923","display_name":"Cheng Hu","orcid":"https://orcid.org/0000-0003-1322-2828"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cheng Hu","raw_affiliation_strings":["School of Mathematics and System Science, Xinjiang University, Urumqi 830017, China"],"raw_orcid":"https://orcid.org/0000-0003-1322-2828","affiliations":[{"raw_affiliation_string":"School of Mathematics and System Science, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035603374"],"corresponding_institution_ids":["https://openalex.org/I4210111575"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.662,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67294892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"16","issue":"2","first_page":"243","last_page":"243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9991999864578247,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9991999864578247,"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":0.9988999962806702,"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":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6568973064422607},{"id":"https://openalex.org/keywords/social-connectedness","display_name":"Social connectedness","score":0.5411268472671509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47795820236206055},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41114088892936707},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3523136377334595},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21571999788284302}],"concepts":[{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6568973064422607},{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.5411268472671509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47795820236206055},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41114088892936707},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3523136377334595},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21571999788284302},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16020243","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020243","pdf_url":"https://www.mdpi.com/2073-8994/16/2/243/pdf?version=1708076967","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:088314a0755d406382a24167a04d9357","is_oa":false,"landing_page_url":"https://doaj.org/article/088314a0755d406382a24167a04d9357","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 2, p 243 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16020243","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020243","pdf_url":"https://www.mdpi.com/2073-8994/16/2/243/pdf?version=1708076967","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320328898","display_name":"Natural Science Foundation of Xinjiang","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391882807.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1146295903","https://openalex.org/W1963812322","https://openalex.org/W1972915842","https://openalex.org/W1983773166","https://openalex.org/W1995058487","https://openalex.org/W1996919229","https://openalex.org/W1998200279","https://openalex.org/W2043630697","https://openalex.org/W2079006313","https://openalex.org/W2099689250","https://openalex.org/W2107396783","https://openalex.org/W2111366290","https://openalex.org/W2111838183","https://openalex.org/W2129248505","https://openalex.org/W2133883778","https://openalex.org/W2142410168","https://openalex.org/W2266296957","https://openalex.org/W2268855328","https://openalex.org/W2346565973","https://openalex.org/W2592852902","https://openalex.org/W2781512642","https://openalex.org/W2963698627","https://openalex.org/W2988685755","https://openalex.org/W3000586685","https://openalex.org/W3016179244","https://openalex.org/W3028041330","https://openalex.org/W3037826211","https://openalex.org/W3046573039","https://openalex.org/W3092876310","https://openalex.org/W3111253645","https://openalex.org/W3112005639","https://openalex.org/W3167229063","https://openalex.org/W3167558821","https://openalex.org/W3199698207","https://openalex.org/W3210031391","https://openalex.org/W3215123515","https://openalex.org/W4308155350","https://openalex.org/W4383108789","https://openalex.org/W4386587209","https://openalex.org/W4391454474","https://openalex.org/W6627322481"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3125761283","https://openalex.org/W2164081328","https://openalex.org/W1976722080","https://openalex.org/W3092556108","https://openalex.org/W2117372696","https://openalex.org/W3152831473","https://openalex.org/W3044931971","https://openalex.org/W1995672666","https://openalex.org/W3008541637"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"a":[3],"robust":[4],"index":[5,51],"named":[6],"first-order":[7],"network":[8,92],"coherence":[9],"(FONC)":[10],"for":[11],"the":[12,23,26,47,50,55,61,72,75,87,90,95,100,105,113,119,120,126],"multi-agent":[13],"systems":[14],"(MASs)":[15],"with":[16,81,99],"layered":[17,43],"lattice-like":[18,44,102],"structure":[19,103],"is":[20,35,52,68],"studied":[21],"via":[22],"angle":[24],"of":[25,33,41,49,57,74,78,89,112],"graph":[27,108],"spectra":[28],"theory.":[29],"The":[30,110],"union":[31],"operation":[32],"graphs":[34],"utilized":[36],"to":[37,85,117],"construct":[38],"two":[39],"pairs":[40],"non-isomorphic":[42],"structures,":[45],"and":[46],"expression":[48],"acquired":[53],"by":[54],"approach":[56],"Laplacian":[58],"spectra,":[59],"then":[60],"corresponding":[62],"asymptotic":[63,97,121],"results":[64],"are":[65],"obtained.":[66],"It":[67],"found":[69],"that":[70],"when":[71],"cardinality":[73],"node":[76],"sets":[77],"coronary":[79],"substructures":[80],"better":[82],"connectedness":[83],"tends":[84],"infinity,":[86],"FONC":[88],"whole":[91],"will":[93],"have":[94],"same":[96],"behavior":[98],"central":[101],"in":[104,125],"considered":[106],"classic":[107],"frameworks.":[109],"indices":[111],"networks":[114],"were":[115],"simulated":[116],"illustrate":[118],"results,":[122],"as":[123],"described":[124],"last":[127],"section.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
