{"id":"https://openalex.org/W4407585905","doi":"https://doi.org/10.1142/s0129626425300016","title":"Normalized Laplacian Spectral Ratio of Graphs","display_name":"Normalized Laplacian Spectral Ratio of Graphs","publication_year":2025,"publication_date":"2025-02-14","ids":{"openalex":"https://openalex.org/W4407585905","doi":"https://doi.org/10.1142/s0129626425300016"},"language":"en","primary_location":{"id":"doi:10.1142/s0129626425300016","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626425300016","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"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":"Parallel Processing Letters","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/A5109298919","display_name":"Cai Min","orcid":null},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Cai","raw_affiliation_strings":["School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai, China","institution_ids":["https://openalex.org/I20616075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110738581","display_name":"J. Wang","orcid":"https://orcid.org/0009-0001-8132-2196"},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JiaJia Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai, China","institution_ids":["https://openalex.org/I20616075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100681909","display_name":"Shumin Zhang","orcid":"https://orcid.org/0009-0001-6681-1127"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shumin Zhang","raw_affiliation_strings":["Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, China","Academy of Plateau Science and Sustainability, People's Government of Qinghai Province and Beijing Normal University, China"],"affiliations":[{"raw_affiliation_string":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"Academy of Plateau Science and Sustainability, People's Government of Qinghai Province and Beijing Normal University, China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100681909"],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05867271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"01n02","first_page":null,"last_page":null},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9696999788284302,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.8240760564804077},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.737499475479126},{"id":"https://openalex.org/keywords/spectral-graph-theory","display_name":"Spectral graph theory","score":0.732127845287323},{"id":"https://openalex.org/keywords/resistance-distance","display_name":"Resistance distance","score":0.6937751173973083},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.617178738117218},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.6118866801261902},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6036673784255981},{"id":"https://openalex.org/keywords/spectral-clustering","display_name":"Spectral clustering","score":0.5795249938964844},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5520187616348267},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5022721290588379},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3628896474838257},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19810977578163147},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1894906461238861},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.1672440469264984},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14354106783866882},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.10460084676742554},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08541721105575562}],"concepts":[{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.8240760564804077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.737499475479126},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.732127845287323},{"id":"https://openalex.org/C612898","wikidata":"https://www.wikidata.org/wiki/Q7315618","display_name":"Resistance distance","level":5,"score":0.6937751173973083},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.617178738117218},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.6118866801261902},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6036673784255981},{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.5795249938964844},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5520187616348267},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5022721290588379},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3628896474838257},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19810977578163147},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1894906461238861},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.1672440469264984},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14354106783866882},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.10460084676742554},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08541721105575562},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"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/s0129626425300016","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626425300016","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"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":"Parallel Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6372693338","display_name":null,"funder_award_id":"12461065","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7471968010","display_name":null,"funder_award_id":"12261074","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":8,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W2014217492","https://openalex.org/W2067632139","https://openalex.org/W2085028691","https://openalex.org/W2153988305","https://openalex.org/W2287993572","https://openalex.org/W3190527535","https://openalex.org/W4237658155"],"related_works":["https://openalex.org/W2081084405","https://openalex.org/W2478475484","https://openalex.org/W3106442811","https://openalex.org/W1002309053","https://openalex.org/W2782821035","https://openalex.org/W2085028691","https://openalex.org/W2389330739","https://openalex.org/W2105661768","https://openalex.org/W4241306937","https://openalex.org/W116988244"],"abstract_inverted_index":{"The":[0,16],"normalized":[1,13,25,36,44,63,77],"Laplacian":[2,14,26,37,45,64,78],"spectrum":[3],"of":[4,10,29,42,48,61,67,81],"a":[5,30,49,59,82],"graph":[6,51,83],"is":[7,33],"the":[8,11,19,22,35,43,55,62,73,76,85],"eigenvalues":[9,28],"associated":[12],"matrix.":[15],"quotient":[17],"between":[18],"largest":[20],"and":[21,70],"second":[23],"smallest":[24],"matrix":[27],"connected":[31,50],"graph,":[32],"called":[34],"spectral":[38,46,65,79],"ratio.":[39],"Some":[40],"bounds":[41],"ratio":[47,66,80],"are":[52],"considered.":[53],"In":[54],"paper,":[56],"we":[57,71],"improve":[58],"relation":[60],"regular":[68],"graphs,":[69],"obtain":[72],"effects":[74],"on":[75],"by":[84],"Operations.":[86]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}