{"id":"https://openalex.org/W2042156180","doi":"https://doi.org/10.1007/s00454-012-9482-9","title":"On the Stretch Factor of Randomly Embedded Random Graphs","display_name":"On the Stretch Factor of Randomly Embedded Random Graphs","publication_year":2012,"publication_date":"2012-12-05","ids":{"openalex":"https://openalex.org/W2042156180","doi":"https://doi.org/10.1007/s00454-012-9482-9","mag":"2042156180"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-012-9482-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9482-9","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9482-9.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9482-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Abbas Mehrabian","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Abbas Mehrabian","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":null,"display_name":"Nick Wormald","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nick Wormald","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.11361234,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"49","issue":"3","first_page":"647","last_page":"658"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.3433000147342682,"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":0.3433000147342682,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.3091999888420105,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.1446000039577484,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6323000192642212},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.6177999973297119},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5745000243186951},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5618000030517578},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.49810001254081726},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4771000146865845},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.46540001034736633},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4178999960422516},{"id":"https://openalex.org/keywords/random-geometric-graph","display_name":"Random geometric graph","score":0.3977000117301941}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7936999797821045},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7645000219345093},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6323000192642212},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.6177999973297119},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5745000243186951},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5618000030517578},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.49810001254081726},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.489300012588501},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4771000146865845},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.46540001034736633},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4178999960422516},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.3977000117301941},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.3880999982357025},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.38350000977516174},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.35260000824928284},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34860000014305115},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3467999994754791},{"id":"https://openalex.org/C159246509","wikidata":"https://www.wikidata.org/wiki/Q5428725","display_name":"Factor graph","level":3,"score":0.3352999985218048},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3237000107765198},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.3179999887943268},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C7605037","wikidata":"https://www.wikidata.org/wiki/Q327164","display_name":"Geometric probability","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C53471067","wikidata":"https://www.wikidata.org/wiki/Q7574076","display_name":"Spatial network","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C54385418","wikidata":"https://www.wikidata.org/wiki/Q2742711","display_name":"Distance","level":4,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-012-9482-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9482-9","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9482-9.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1205.6252","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.6252","pdf_url":"https://arxiv.org/pdf/1205.6252","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-012-9482-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9482-9","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9482-9.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320994","display_name":"Canada Research Chairs","ror":"https://ror.org/0517h6h17"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2042156180.pdf","grobid_xml":"https://content.openalex.org/works/W2042156180.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W630423399","https://openalex.org/W1505970908","https://openalex.org/W1512460878","https://openalex.org/W2478722229"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2016-06-24T00:00:00"}