{"id":"https://openalex.org/W2064729727","doi":"https://doi.org/10.1007/s11134-012-9276-z","title":"On the distribution of typical shortest-path lengths in connected random geometric graphs","display_name":"On the distribution of typical shortest-path lengths in connected random geometric graphs","publication_year":2012,"publication_date":"2012-02-01","ids":{"openalex":"https://openalex.org/W2064729727","doi":"https://doi.org/10.1007/s11134-012-9276-z","mag":"2064729727"},"language":"en","primary_location":{"id":"doi:10.1007/s11134-012-9276-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11134-012-9276-z","pdf_url":null,"source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","1572-9443"],"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":"Queueing Systems","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/A5053962980","display_name":"David Neuh\u00e4user","orcid":null},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"D. Neuh\u00e4user","raw_affiliation_strings":["Institute of Stochastics, Ulm University, 89069, Ulm, Germany","Institute of Stochastics, Ulm University, Ulm, Germany 89069#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Stochastics, Ulm University, 89069, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]},{"raw_affiliation_string":"Institute of Stochastics, Ulm University, Ulm, Germany 89069#TAB#","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102710500","display_name":"Christian Hirsch","orcid":"https://orcid.org/0000-0003-4136-3740"},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"C. Hirsch","raw_affiliation_strings":["Institute of Stochastics, Ulm University, 89069, Ulm, Germany","Institute of Stochastics, Ulm University, Ulm, Germany 89069#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Stochastics, Ulm University, 89069, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]},{"raw_affiliation_string":"Institute of Stochastics, Ulm University, Ulm, Germany 89069#TAB#","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053891417","display_name":"Catherine Gloaguen","orcid":null},"institutions":[{"id":"https://openalex.org/I19370010","display_name":"Orange (France)","ror":"https://ror.org/035j0tq82","country_code":"FR","type":"company","lineage":["https://openalex.org/I19370010"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"C. Gloaguen","raw_affiliation_strings":["Orange Labs, 38-40, rue du G\u00e9n\u00e9ral Leclerc, 92794, Issy-les-Moulineaux, France","Orange Labs, Issy-les-Moulineaux, France 92794#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Orange Labs, 38-40, rue du G\u00e9n\u00e9ral Leclerc, 92794, Issy-les-Moulineaux, France","institution_ids":["https://openalex.org/I19370010"]},{"raw_affiliation_string":"Orange Labs, Issy-les-Moulineaux, France 92794#TAB#","institution_ids":["https://openalex.org/I19370010"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042036645","display_name":"Volker Schmidt","orcid":"https://orcid.org/0000-0001-7451-8185"},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"V. Schmidt","raw_affiliation_strings":["Institute of Stochastics, Ulm University, 89069, Ulm, Germany","Institute of Stochastics, Ulm University, Ulm, Germany 89069#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Stochastics, Ulm University, 89069, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]},{"raw_affiliation_string":"Institute of Stochastics, Ulm University, Ulm, Germany 89069#TAB#","institution_ids":["https://openalex.org/I196349391"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.144,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.93944363,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"71","issue":"1-2","first_page":"199","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.9501000046730042,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.804542064666748},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7122710943222046},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.6269779205322266},{"id":"https://openalex.org/keywords/distance","display_name":"Distance","score":0.4861847758293152},{"id":"https://openalex.org/keywords/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.4652671813964844},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.463002473115921},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.44524332880973816},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4170057773590088},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3927803039550781},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2673953175544739},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20907849073410034}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.804542064666748},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7122710943222046},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.6269779205322266},{"id":"https://openalex.org/C54385418","wikidata":"https://www.wikidata.org/wiki/Q2742711","display_name":"Distance","level":4,"score":0.4861847758293152},{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.4652671813964844},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.463002473115921},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.44524332880973816},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4170057773590088},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3927803039550781},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2673953175544739},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20907849073410034},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11134-012-9276-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11134-012-9276-z","pdf_url":null,"source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","1572-9443"],"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":"Queueing Systems","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/6e4e358c-f481-4d37-9ef6-6553d439259d","is_oa":false,"landing_page_url":"https://pure.au.dk/portal/en/publications/6e4e358c-f481-4d37-9ef6-6553d439259d","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Neuh\u00e4user, D, Hirsch, C, Gloaguen, C & Schmidt, V 2012, 'On the distribution of typical shortest-path lengths in connected random geometric graphs', Queueing Systems, bind 71, nr. 1, s. 199-220.","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320325530","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W565214016","https://openalex.org/W630423399","https://openalex.org/W1510924284","https://openalex.org/W1578430072","https://openalex.org/W1604071614","https://openalex.org/W1986994624","https://openalex.org/W1987229010","https://openalex.org/W1992707502","https://openalex.org/W1998476184","https://openalex.org/W1999712605","https://openalex.org/W2050966639","https://openalex.org/W2052197092","https://openalex.org/W2053778555","https://openalex.org/W2118166339","https://openalex.org/W2152434295","https://openalex.org/W2317392131","https://openalex.org/W2484039423","https://openalex.org/W2797135730","https://openalex.org/W3104975753","https://openalex.org/W4211083695","https://openalex.org/W4233064940","https://openalex.org/W4298909978"],"related_works":["https://openalex.org/W2059217232","https://openalex.org/W1992160534","https://openalex.org/W2371724110","https://openalex.org/W2885312149","https://openalex.org/W1930867958","https://openalex.org/W2053576657","https://openalex.org/W4206423751","https://openalex.org/W2041214247","https://openalex.org/W1995318580","https://openalex.org/W2133344964"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}