{"id":"https://openalex.org/W2943330257","doi":"https://doi.org/10.1142/s1793830919500319","title":"Normalized algebraic connectivity of graphs","display_name":"Normalized algebraic connectivity of graphs","publication_year":2019,"publication_date":"2019-03-24","ids":{"openalex":"https://openalex.org/W2943330257","doi":"https://doi.org/10.1142/s1793830919500319","mag":"2943330257"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830919500319","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500319","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5047297187","display_name":"Hongjuan Liu","orcid":"https://orcid.org/0000-0001-8815-9355"},"institutions":[{"id":"https://openalex.org/I53592917","display_name":"Jiangxi Normal University","ror":"https://ror.org/05nkgk822","country_code":"CN","type":"education","lineage":["https://openalex.org/I53592917"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongjuan Liu","raw_affiliation_strings":["College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, P. R. China","institution_ids":["https://openalex.org/I53592917"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101454283","display_name":"Honghai Li","orcid":"https://orcid.org/0000-0002-2498-250X"},"institutions":[{"id":"https://openalex.org/I53592917","display_name":"Jiangxi Normal University","ror":"https://ror.org/05nkgk822","country_code":"CN","type":"education","lineage":["https://openalex.org/I53592917"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Honghai Li","raw_affiliation_strings":["College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, P. R. China","institution_ids":["https://openalex.org/I53592917"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047297187"],"corresponding_institution_ids":["https://openalex.org/I53592917"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12527202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"03","first_page":"1950031","last_page":"1950031"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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"}},{"id":"https://openalex.org/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10083","display_name":"Graphene research and applications","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.9243900775909424},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.7647775411605835},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6715307235717773},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5875978469848633},{"id":"https://openalex.org/keywords/algebraic-graph-theory","display_name":"Algebraic graph theory","score":0.5833176374435425},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5559405088424683},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5291120409965515},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49837470054626465},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49297142028808594},{"id":"https://openalex.org/keywords/coalescence","display_name":"Coalescence (physics)","score":0.4871830344200134},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4370863437652588},{"id":"https://openalex.org/keywords/algebraic-properties","display_name":"Algebraic properties","score":0.42620033025741577},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4150039553642273},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10362666845321655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0756554901599884}],"concepts":[{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.9243900775909424},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.7647775411605835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6715307235717773},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5875978469848633},{"id":"https://openalex.org/C25799778","wikidata":"https://www.wikidata.org/wiki/Q4724003","display_name":"Algebraic graph theory","level":3,"score":0.5833176374435425},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5559405088424683},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5291120409965515},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49837470054626465},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49297142028808594},{"id":"https://openalex.org/C149792144","wikidata":"https://www.wikidata.org/wiki/Q2071902","display_name":"Coalescence (physics)","level":2,"score":0.4871830344200134},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4370863437652588},{"id":"https://openalex.org/C2989065042","wikidata":"https://www.wikidata.org/wiki/Q7378971","display_name":"Algebraic properties","level":2,"score":0.42620033025741577},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4150039553642273},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10362666845321655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0756554901599884},{"id":"https://openalex.org/C87355193","wikidata":"https://www.wikidata.org/wiki/Q411","display_name":"Astrobiology","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":1,"locations":[{"id":"doi:10.1142/s1793830919500319","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500319","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"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":13,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1499564662","https://openalex.org/W1965091154","https://openalex.org/W1985241192","https://openalex.org/W1991994646","https://openalex.org/W2045298704","https://openalex.org/W2049435936","https://openalex.org/W2127769624","https://openalex.org/W2193378305","https://openalex.org/W2417348321","https://openalex.org/W2430629946","https://openalex.org/W2570176964","https://openalex.org/W2766907662"],"related_works":["https://openalex.org/W2001476852","https://openalex.org/W4205812024","https://openalex.org/W2129123449","https://openalex.org/W1557246723","https://openalex.org/W2111424493","https://openalex.org/W2475700395","https://openalex.org/W3091808089","https://openalex.org/W2478475484","https://openalex.org/W4368408228","https://openalex.org/W2117285924"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,14,23],"see":[2,15,24],"text]":[3],"be":[4],"the":[5,18,31,34,39,54,60],"second":[6],"smallest":[7],"normalized":[8,19,35,55],"Laplacian":[9],"eigenvalue":[10],"of":[11,22,38,41,46],"a":[12],"graph":[13,61],"text],":[16],"called":[17],"algebraic":[20,36,56],"connectivity":[21,37,57],"text].":[25],"In":[26],"this":[27],"paper,":[28],"we":[29,51],"study":[30],"relation":[32],"between":[33],"coalescence":[40],"two":[42,48],"graphs":[43],"and":[44],"that":[45],"these":[47],"graphs.":[49],"Furthermore,":[50],"investigate":[52],"how":[53],"behaves":[58],"when":[59],"is":[62],"perturbed":[63],"by":[64],"relocating":[65],"pendent":[66],"edges.":[67]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
