{"id":"https://openalex.org/W2021155376","doi":"https://doi.org/10.1007/s00454-013-9558-1","title":"Ollivier\u2019s Ricci Curvature, Local Clustering and Curvature-Dimension Inequalities on Graphs","display_name":"Ollivier\u2019s Ricci Curvature, Local Clustering and Curvature-Dimension Inequalities on Graphs","publication_year":2013,"publication_date":"2013-11-12","ids":{"openalex":"https://openalex.org/W2021155376","doi":"https://doi.org/10.1007/s00454-013-9558-1","mag":"2021155376"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-013-9558-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-013-9558-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-013-9558-1.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":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-013-9558-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072990982","display_name":"J\u00fcrgen Jost","orcid":"https://orcid.org/0000-0001-5258-6590"},"institutions":[{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]},{"id":"https://openalex.org/I147765834","display_name":"Leipzig University of Applied Sciences","ror":"https://ror.org/03xgcq477","country_code":"DE","type":"education","lineage":["https://openalex.org/I147765834"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]},{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"J\u00fcrgen Jost","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, University of Leipzig, Leipzig, 04103, Germany","Max Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany","Santa Fe Institute for the Sciences of Complexity, Santa Fe, NM, 87501, USA","Max Planck Institute for Mathematics in the Sciences","Santa Fe Institute for the Sciences of Complexity","University of Leipzig"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, University of Leipzig, Leipzig, 04103, Germany","institution_ids":["https://openalex.org/I147765834","https://openalex.org/I926574661"]},{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany","institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"]},{"raw_affiliation_string":"Santa Fe Institute for the Sciences of Complexity, Santa Fe, NM, 87501, USA","institution_ids":["https://openalex.org/I1308548392"]},{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences","institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"]},{"raw_affiliation_string":"Santa Fe Institute for the Sciences of Complexity","institution_ids":["https://openalex.org/I1308548392"]},{"raw_affiliation_string":"University of Leipzig","institution_ids":["https://openalex.org/I926574661"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101517415","display_name":"Shiping Liu","orcid":"https://orcid.org/0000-0002-9987-1935"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN","DE","GB"],"is_corresponding":true,"raw_author_name":"Shiping Liu","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China","Max Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany","Chinese Academy of Sciences","Durham University","Max Planck Institute for Mathematics in the Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany","institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"]},{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"Durham University","institution_ids":["https://openalex.org/I190082696"]},{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences","institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5101517415"],"corresponding_institution_ids":["https://openalex.org/I190082696","https://openalex.org/I19820366","https://openalex.org/I4210091327","https://openalex.org/I4210119712","https://openalex.org/I4210120485"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":11.6274,"has_fulltext":true,"cited_by_count":195,"citation_normalized_percentile":{"value":0.9919504,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"51","issue":"2","first_page":"300","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9988999962806702,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9988999962806702,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9952999949455261,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9900000095367432,"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/ricci-curvature","display_name":"Ricci curvature","score":0.8785663843154907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8470087647438049},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.7027326822280884},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5498190522193909},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5399901866912842},{"id":"https://openalex.org/keywords/riemann-curvature-tensor","display_name":"Riemann curvature tensor","score":0.4241527318954468},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4076094925403595},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32953667640686035},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15860062837600708}],"concepts":[{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.8785663843154907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8470087647438049},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.7027326822280884},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5498190522193909},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5399901866912842},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.4241527318954468},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4076094925403595},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32953667640686035},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15860062837600708}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-013-9558-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-013-9558-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-013-9558-1.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:CiteSeerX.psu:10.1.1.771.5394","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.771.5394","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1103.4037.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:708444","is_oa":false,"landing_page_url":"http://edoc.mpg.de/708444","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, v.51, 300-322 (2014)","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s00454-013-9558-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-013-9558-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-013-9558-1.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":[{"score":0.4300000071525574,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G3207356259","display_name":null,"funder_award_id":"2007\u20132013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G393177772","display_name":null,"funder_award_id":"FP7 2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5702163051","display_name":null,"funder_award_id":"FP7/2007","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2021155376.pdf","grobid_xml":"https://content.openalex.org/works/W2021155376.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W145503409","https://openalex.org/W385466589","https://openalex.org/W1488972097","https://openalex.org/W1511217050","https://openalex.org/W1525296983","https://openalex.org/W1578099820","https://openalex.org/W1585160083","https://openalex.org/W1967200178","https://openalex.org/W1968781546","https://openalex.org/W1972309199","https://openalex.org/W1972708599","https://openalex.org/W2000124739","https://openalex.org/W2006943386","https://openalex.org/W2007338883","https://openalex.org/W2033894891","https://openalex.org/W2039258749","https://openalex.org/W2043694962","https://openalex.org/W2045049746","https://openalex.org/W2046267801","https://openalex.org/W2064759795","https://openalex.org/W2077810240","https://openalex.org/W2087667141","https://openalex.org/W2095922668","https://openalex.org/W2112090702","https://openalex.org/W2334471843","https://openalex.org/W2936788301","https://openalex.org/W2964129753","https://openalex.org/W2964133817","https://openalex.org/W4233762729","https://openalex.org/W4236312485","https://openalex.org/W4248500611","https://openalex.org/W4285719527","https://openalex.org/W4292082790"],"related_works":["https://openalex.org/W2058655323","https://openalex.org/W2254577414","https://openalex.org/W3104800576","https://openalex.org/W2946879650","https://openalex.org/W2604503417","https://openalex.org/W2024803319","https://openalex.org/W2087358568","https://openalex.org/W4387382666","https://openalex.org/W120930426","https://openalex.org/W4312212642"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":24},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":23},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}