{"id":"https://openalex.org/W2108797586","doi":"https://doi.org/10.1007/978-3-540-78808-9_3","title":"Expansion and Lack Thereof in Randomly Perturbed Graphs","display_name":"Expansion and Lack Thereof in Randomly Perturbed Graphs","publication_year":2008,"publication_date":"2008-08-12","ids":{"openalex":"https://openalex.org/W2108797586","doi":"https://doi.org/10.1007/978-3-540-78808-9_3","mag":"2108797586"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-78808-9_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-78808-9_3","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5055212893","display_name":"Abraham D. Flaxman","orcid":"https://orcid.org/0000-0001-6033-4713"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Abraham D. Flaxman","raw_affiliation_strings":["Microsoft Research, Redmond, WA, USA, 98052","Microsoft Research, Redmond, USA 98052#TAB#"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Redmond, WA, USA, 98052","institution_ids":["https://openalex.org/I1290206253"]},{"raw_affiliation_string":"Microsoft Research, Redmond, USA 98052#TAB#","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055212893"],"corresponding_institution_ids":["https://openalex.org/I1290206253"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":18.4447,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.99391172,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"24","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10772","display_name":"Distributed systems and fault tolerance","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.625617265701294},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5956926345825195},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5561034083366394},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.495919793844223},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4434269666671753},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4216436743736267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42052173614501953},{"id":"https://openalex.org/keywords/null-graph","display_name":"Null graph","score":0.41237393021583557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3973812758922577},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.3680081367492676},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.3614594340324402}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.625617265701294},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5956926345825195},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5561034083366394},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.495919793844223},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4434269666671753},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4216436743736267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42052173614501953},{"id":"https://openalex.org/C17169500","wikidata":"https://www.wikidata.org/wiki/Q3033506","display_name":"Null graph","level":5,"score":0.41237393021583557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3973812758922577},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.3680081367492676},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3614594340324402},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-540-78808-9_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-78808-9_3","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CULeuclid:euclid.im/1243430603","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.im/1243430603","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:10.1.1.495.9792","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.495.9792","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/pubs/70332/tr-2006-118.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":60,"referenced_works":["https://openalex.org/W100944330","https://openalex.org/W179403124","https://openalex.org/W1489617709","https://openalex.org/W1520007244","https://openalex.org/W1524198677","https://openalex.org/W1565689800","https://openalex.org/W1589703745","https://openalex.org/W1599622173","https://openalex.org/W1631603072","https://openalex.org/W1928413254","https://openalex.org/W1964402547","https://openalex.org/W1968939650","https://openalex.org/W1969080501","https://openalex.org/W1976969221","https://openalex.org/W1993111701","https://openalex.org/W1993418693","https://openalex.org/W1994840070","https://openalex.org/W1995885398","https://openalex.org/W2004943036","https://openalex.org/W2006605460","https://openalex.org/W2016918503","https://openalex.org/W2021145763","https://openalex.org/W2026709222","https://openalex.org/W2029013046","https://openalex.org/W2034053794","https://openalex.org/W2037653791","https://openalex.org/W2057444879","https://openalex.org/W2058699951","https://openalex.org/W2064782937","https://openalex.org/W2065630310","https://openalex.org/W2068871408","https://openalex.org/W2069992656","https://openalex.org/W2072211488","https://openalex.org/W2078523165","https://openalex.org/W2079035346","https://openalex.org/W2088164510","https://openalex.org/W2088668624","https://openalex.org/W2112090702","https://openalex.org/W2118625817","https://openalex.org/W2123718282","https://openalex.org/W2128678576","https://openalex.org/W2129497745","https://openalex.org/W2151221105","https://openalex.org/W2152361742","https://openalex.org/W2165341195","https://openalex.org/W2181086294","https://openalex.org/W2478722229","https://openalex.org/W2496163386","https://openalex.org/W2595295261","https://openalex.org/W2624048597","https://openalex.org/W2770485470","https://openalex.org/W2911437840","https://openalex.org/W3100678396","https://openalex.org/W3105870018","https://openalex.org/W3144881883","https://openalex.org/W4230202685","https://openalex.org/W4233055081","https://openalex.org/W4243880374","https://openalex.org/W4247942259","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2954009223","https://openalex.org/W1568744482","https://openalex.org/W2366079443","https://openalex.org/W1927597435","https://openalex.org/W2793949464","https://openalex.org/W4379539820","https://openalex.org/W153309283","https://openalex.org/W2380035736","https://openalex.org/W2741713059","https://openalex.org/W4299307887"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}