{"id":"https://openalex.org/W2054945981","doi":"https://doi.org/10.1080/15427951.2007.10129296","title":"The Spectral Gap of a Random Subgraph of a Graph","display_name":"The Spectral Gap of a Random Subgraph of a Graph","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2054945981","doi":"https://doi.org/10.1080/15427951.2007.10129296","mag":"2054945981"},"language":"en","primary_location":{"id":"doi:10.1080/15427951.2007.10129296","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129296","pdf_url":"https://www.internetmathematicsjournal.com/article/1444.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.internetmathematicsjournal.com/article/1444.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113657664","display_name":"Fan Chung","orcid":"https://orcid.org/0000-0002-6553-7402"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fan Chung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029310944","display_name":"Paul Horn","orcid":"https://orcid.org/0000-0003-3022-9036"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul Horn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4424,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.62146249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"4","issue":"2-3","first_page":"225","last_page":"244"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9991999864578247,"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":0.9991999864578247,"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":0.995199978351593,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9898999929428101,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8987629413604736},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7669626474380493},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.7329095005989075},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6158534288406372},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6060590744018555},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.480495810508728},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"Graph factorization","score":0.4702264964580536},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.47019872069358826},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4211472272872925},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.17529278993606567},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.1480024755001068},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07240068912506104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07056710124015808},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05138102173805237}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8987629413604736},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7669626474380493},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.7329095005989075},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6158534288406372},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6060590744018555},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.480495810508728},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.4702264964580536},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.47019872069358826},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4211472272872925},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.17529278993606567},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.1480024755001068},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07240068912506104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07056710124015808},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05138102173805237}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/15427951.2007.10129296","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129296","pdf_url":"https://www.internetmathematicsjournal.com/article/1444.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.im/1243430607","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.im/1243430607","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.205.1604","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.205.1604","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucsd.edu/%7Ephorn/randomsub.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1080/15427951.2007.10129296","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129296","pdf_url":"https://www.internetmathematicsjournal.com/article/1444.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4514709479","display_name":"ITR Collaborative Research:  ASE-DMC  Computational complexity for interactive computing","funder_award_id":"0426858","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7569553291","display_name":"Spectral and probabilistic methods for large sparse graphs","funder_award_id":"0457215","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054945981.pdf","grobid_xml":"https://content.openalex.org/works/W2054945981.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W638149299","https://openalex.org/W1578099820","https://openalex.org/W1639593279","https://openalex.org/W1967780722","https://openalex.org/W1973836644","https://openalex.org/W1993418693","https://openalex.org/W2014075779","https://openalex.org/W2029948740","https://openalex.org/W2088164510","https://openalex.org/W2107016171","https://openalex.org/W2112643910","https://openalex.org/W2328187444","https://openalex.org/W2611581392","https://openalex.org/W3098555975","https://openalex.org/W4235584939"],"related_works":["https://openalex.org/W2560376394","https://openalex.org/W2766368564","https://openalex.org/W822020258","https://openalex.org/W4299378864","https://openalex.org/W2953336627","https://openalex.org/W2963346002","https://openalex.org/W124672475","https://openalex.org/W3099059030","https://openalex.org/W2054945981","https://openalex.org/W2793671626"],"abstract_inverted_index":{"We":[0],"examine":[1],"the":[2],"relationship":[3],"of":[4,33,49],"a":[5,27,46],"graph":[6],"_G_":[7,25,50],"and":[8,37],"its":[9,34,62],"random":[10,47],"subgraphs,":[11],"which":[12],"are":[13],"defined":[14],"by":[15],"independently":[16],"choosing":[17],"each":[18],"edge":[19],"with":[20,54],"probability":[21,56],"_p_.":[22],"Suppose":[23],"that":[24,45],"has":[26,60],"spectral":[28,63],"gap":[29,64],"\u03bb":[30],"(in":[31],"terms":[32],"normalized":[35],"Laplacian)":[36],"minimum":[38],"degree":[39],"_d_<sub>min</sub>.":[40],"Then":[41],"we":[42],"can":[43],"show":[44],"subgraph":[48],"on":[51],"_n_":[52],"vertices":[53],"edge-selection":[55],"_p_":[57],"almost":[58],"surely":[59],"as":[61],"<inline-graphic":[65],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"":[66],"xlink:href=\"uinm_a_10129296_o_ilf0001.gif\"></inline-graphic>.":[67]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}