{"id":"https://openalex.org/W1631603072","doi":"https://doi.org/10.1007/bf02579166","title":"Eigenvalues and expanders","display_name":"Eigenvalues and expanders","publication_year":1986,"publication_date":"1986-06-01","ids":{"openalex":"https://openalex.org/W1631603072","doi":"https://doi.org/10.1007/bf02579166","mag":"1631603072"},"language":"en","primary_location":{"id":"doi:10.1007/bf02579166","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02579166","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","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/A5055817232","display_name":"Ilan Alon","orcid":"https://orcid.org/0000-0002-6927-593X"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["IL","US"],"is_corresponding":true,"raw_author_name":"Noga Alon","raw_affiliation_strings":["Department of Mathematics, Massachusetts Inst. of Technology, 02139, Cambridge, MA, USA","Department of Mathematics, Tel Aviv University, 69978, Ramat Aviv, Tel Aviv, Israel","Department of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel","Department of Mathematics, Massachusetts Inst. of Technology, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Inst. of Technology, 02139, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics, Tel Aviv University, 69978, Ramat Aviv, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Department of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Department of Mathematics, Massachusetts Inst. of Technology, Cambridge, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055817232"],"corresponding_institution_ids":["https://openalex.org/I16391192","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":20.0273,"has_fulltext":false,"cited_by_count":1164,"citation_normalized_percentile":{"value":0.99636253,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"6","issue":"2","first_page":"83","last_page":"96"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T11716","display_name":"Random Matrices and Applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9991000294685364,"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":0.8208844661712646},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8109849691390991},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.7882288694381714},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7725820541381836},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5647017359733582},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4889472723007202},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4403552711009979},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3958863914012909}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8208844661712646},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8109849691390991},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.7882288694381714},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7725820541381836},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5647017359733582},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4889472723007202},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4403552711009979},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3958863914012909},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf02579166","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02579166","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.300.3922","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.300.3922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~nogaa/PDFS/Publications2/Eigenvalues and expanders.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W100944330","https://openalex.org/W593649846","https://openalex.org/W1485507727","https://openalex.org/W1515707356","https://openalex.org/W1587590810","https://openalex.org/W1587744656","https://openalex.org/W1968864043","https://openalex.org/W1969907247","https://openalex.org/W1993111701","https://openalex.org/W2018566183","https://openalex.org/W2021496873","https://openalex.org/W2028816357","https://openalex.org/W2031246048","https://openalex.org/W2035155528","https://openalex.org/W2040709138","https://openalex.org/W2048958388","https://openalex.org/W2057146791","https://openalex.org/W2066161457","https://openalex.org/W2066947547","https://openalex.org/W2077054189","https://openalex.org/W2084751542","https://openalex.org/W2088164510","https://openalex.org/W2091476183","https://openalex.org/W2092198261","https://openalex.org/W2121284046","https://openalex.org/W2328187444","https://openalex.org/W4235082445"],"related_works":["https://openalex.org/W154856185","https://openalex.org/W4377019474","https://openalex.org/W2602709848","https://openalex.org/W4281939267","https://openalex.org/W2091826982","https://openalex.org/W2036057584","https://openalex.org/W2107875203","https://openalex.org/W245205139","https://openalex.org/W2038143369","https://openalex.org/W4240697234"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":29},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":25},{"year":2022,"cited_by_count":47},{"year":2021,"cited_by_count":40},{"year":2020,"cited_by_count":67},{"year":2019,"cited_by_count":48},{"year":2018,"cited_by_count":34},{"year":2017,"cited_by_count":31},{"year":2016,"cited_by_count":36},{"year":2015,"cited_by_count":52},{"year":2014,"cited_by_count":49},{"year":2013,"cited_by_count":53},{"year":2012,"cited_by_count":40}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}