{"id":"https://openalex.org/W1565832774","doi":"https://doi.org/10.37236/227","title":"The Spectral Gap of Random Graphs with Given Expected Degrees","display_name":"The Spectral Gap of Random Graphs with Given Expected Degrees","publication_year":2009,"publication_date":"2009-11-13","ids":{"openalex":"https://openalex.org/W1565832774","doi":"https://doi.org/10.37236/227","mag":"1565832774"},"language":"en","primary_location":{"id":"doi:10.37236/227","is_oa":true,"landing_page_url":"https://doi.org/10.37236/227","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r138/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r138/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044991483","display_name":"Amin Coja\u2010Oghlan","orcid":"https://orcid.org/0000-0002-7350-1418"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Amin Coja-Oghlan","raw_affiliation_strings":["University of Edinburgh, School of Informatics Crichton Street, Edinburgh EH8 9AB, UK"],"affiliations":[{"raw_affiliation_string":"University of Edinburgh, School of Informatics Crichton Street, Edinburgh EH8 9AB, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055693000","display_name":"Andr\u00e9 Lanka","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Lanka","raw_affiliation_strings":["Technische Universitt Chemnitz, Fakultt fr Informatik Strae der Nationen 62, 09107 Chemnitz, Germany","Technische Universit\u00e4t Chemnitz, Fakult\u00e4t f\u00fcr Informatik Stra\u00dfe der Nationen 62, 09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Technische Universitt Chemnitz, Fakultt fr Informatik Strae der Nationen 62, 09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]},{"raw_affiliation_string":"Technische Universit\u00e4t Chemnitz, Fakult\u00e4t f\u00fcr Informatik Stra\u00dfe der Nationen 62, 09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044991483"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":3.8749,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.93224452,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"1","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":0.9804999828338623,"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":0.9804999828338623,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9343000054359436,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9240000247955322,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/combinatorics","display_name":"Combinatorics","score":0.8548353314399719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8106309175491333},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6488502025604248},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.6137523651123047},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5623811483383179},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5573552846908569},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5295302271842957},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4793872833251953},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4245571494102478},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41284775733947754},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1357986032962799},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10286939144134521}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8548353314399719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8106309175491333},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6488502025604248},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.6137523651123047},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5623811483383179},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5573552846908569},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5295302271842957},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4793872833251953},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4245571494102478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41284775733947754},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1357986032962799},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10286939144134521},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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:10.37236/227","is_oa":true,"landing_page_url":"https://doi.org/10.37236/227","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r138/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/227","is_oa":true,"landing_page_url":"https://doi.org/10.37236/227","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r138/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1565832774.pdf","grobid_xml":"https://content.openalex.org/works/W1565832774.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1532006000","https://openalex.org/W1572923654","https://openalex.org/W1574864566","https://openalex.org/W1605711022","https://openalex.org/W1973836644","https://openalex.org/W2003134180","https://openalex.org/W2026709222","https://openalex.org/W2045756072","https://openalex.org/W2079035346","https://openalex.org/W2088164510","https://openalex.org/W2089710678","https://openalex.org/W2090731451","https://openalex.org/W2112976607","https://openalex.org/W2114030927","https://openalex.org/W2124637492","https://openalex.org/W2328187444","https://openalex.org/W4241998900","https://openalex.org/W4242291765","https://openalex.org/W4243880374","https://openalex.org/W4253491426","https://openalex.org/W6779388081"],"related_works":["https://openalex.org/W2921748058","https://openalex.org/W2030922374","https://openalex.org/W2560376394","https://openalex.org/W2766368564","https://openalex.org/W822020258","https://openalex.org/W4299378864","https://openalex.org/W2056196261","https://openalex.org/W2953336627","https://openalex.org/W2963346002","https://openalex.org/W124672475"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,35,39,60,81],"Laplacian":[3,41],"eigenvalues":[4],"of":[5,38,42,83],"a":[6,12,28,54],"random":[7],"graph":[8],"$G(n,\\vec":[9,25],"d)$":[10,26],"with":[11,48,72],"given":[13],"expected":[14,62],"degree":[15],"distribution":[16],"$\\vec":[17],"d$.":[18],"The":[19,64,77],"main":[20],"result":[21,65],"is":[22,45,53],"that":[23,34],"w.h.p.":[24],"has":[27],"large":[29],"subgraph":[30],"core$(G(n,\\vec":[31,43],"d))$":[32,44],"such":[33],"spectral":[36],"gap":[37],"normalized":[40],"$\\geq1-c_0\\bar":[46],"d_{\\min}^{-1/2}$":[47],"high":[49],"probability;":[50],"here":[51],"$c_0&gt;0$":[52],"constant,":[55],"and":[56,86],"$\\bar":[57,73],"d_{\\min}$":[58],"signifies":[59],"minimum":[61],"degree.":[63],"in":[66],"particular":[67],"applies":[68],"to":[69],"sparse":[70],"graphs":[71],"d_{\\min}=O(1)$":[74],"as":[75],"$n\\rightarrow\\infty$.":[76],"present":[78],"paper":[79],"complements":[80],"work":[82],"Chung,":[84],"Lu,":[85],"Vu":[87],"[Internet":[88],"Mathematics":[89],"1,":[90],"2003].":[91]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
