{"id":"https://openalex.org/W4404401232","doi":"https://doi.org/10.1142/s0219199726500823","title":"Evolution of weights on a connected finite graph","display_name":"Evolution of weights on a connected finite graph","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W4404401232","doi":"https://doi.org/10.1142/s0219199726500823"},"language":"en","primary_location":{"id":"doi:10.1142/s0219199726500823","doi":"https://doi.org/10.1142/s0219199726500823","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219199726500823","pdf_url":null,"source":{"id":"https://openalex.org/S51811661","display_name":"Communications in Contemporary Mathematics","issn_l":"0219-1997","issn":["0219-1997","1793-6683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Contemporary Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2411.06393","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035996979","display_name":"Jicheng Ma","orcid":"https://orcid.org/0000-0001-9293-6057","observed_orcids":["https://orcid.org/0000-0001-9293-6057","https://orcid.org/0000-0002-4020-8514"]},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jicheng Ma","raw_affiliation_strings":["School of Mathematics, Renmin University of China, Beijing 100872, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-4020-8514","affiliations":[{"raw_affiliation_string":"School of Mathematics, Renmin University of China, Beijing 100872, P. R. China","institution_ids":["https://openalex.org/I78988378"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109431625","display_name":"Yunyan Yang","orcid":"https://orcid.org/0000-0002-9520-6639","observed_orcids":["https://orcid.org/0000-0002-9520-6639"]},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunyan Yang","raw_affiliation_strings":["School of Mathematics, Renmin University of China, Beijing 100872, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-9520-6639","affiliations":[{"raw_affiliation_string":"School of Mathematics, Renmin University of China, Beijing 100872, P. R. China","institution_ids":["https://openalex.org/I78988378"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78988378"],"apc_list":null,"apc_paid":null,"fwci":15.2214,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.99261993,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","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/T10064","display_name":"Complex Network Analysis Techniques","score":9.999999747378752e-05,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ollivier-ricci-curvature","display_name":"Ollivier-Ricci curvature","score":0.8550000190734863},{"id":"https://openalex.org/keywords/wasserstein-distance","display_name":"Wasserstein distance","score":0.7689999938011169},{"id":"https://openalex.org/keywords/lazy-random-walk","display_name":"lazy random walk","score":0.8019999861717224},{"id":"https://openalex.org/keywords/discrete-ricci-flow","display_name":"discrete Ricci flow","score":0.6470000147819519},{"id":"https://openalex.org/keywords/community-detection","display_name":"community detection","score":0.6629999876022339},{"id":"https://openalex.org/keywords/finite-graphs","display_name":"finite graphs","score":0.5289999842643738}],"concepts":[{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5498188138008118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41258031129837036},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3764444589614868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33502888679504395}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0219199726500823","doi":"https://doi.org/10.1142/s0219199726500823","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219199726500823","pdf_url":null,"source":{"id":"https://openalex.org/S51811661","display_name":"Communications in Contemporary Mathematics","issn_l":"0219-1997","issn":["0219-1997","1793-6683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Contemporary Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2411.06393","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2411.06393","pdf_url":"https://arxiv.org/pdf/2411.06393","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2411.06393","doi":"https://doi.org/10.48550/arxiv.2411.06393","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2411.06393","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2411.06393","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2411.06393","pdf_url":"https://arxiv.org/pdf/2411.06393","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322499","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4404401232.pdf","grobid_xml":"https://content.openalex.org/works/W4404401232.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1970564715","https://openalex.org/W4380372182","https://openalex.org/W4406783563","https://openalex.org/W4413930065","https://openalex.org/W7125400924"],"related_works":["https://openalex.org/W4413930065","https://openalex.org/W4415328942","https://openalex.org/W7166126337","https://openalex.org/W7153242617","https://openalex.org/W4220858736","https://openalex.org/W7216595954","https://openalex.org/W7203713055","https://openalex.org/W4416222555","https://openalex.org/W2552074115","https://openalex.org/W7147238919"],"abstract_inverted_index":{"On":[0],"a":[1,16,72,89,114],"connected":[2],"finite":[3],"graph,":[4],"we":[5,81],"propose":[6],"an":[7,57,64],"evolution":[8,21,99],"of":[9,28,30,96,105],"weights":[10],"including":[11],"Ollivier\u2019s":[12],"Ricci":[13,173],"flow":[14],"as":[15,56,122],"special":[17],"case.":[18],"During":[19],"the":[20,26,34,37,50,78,84,97,103,139,158],"process,":[22],"on":[23,77,112,171],"each":[24],"edge,":[25],"speed":[27],"change":[29],"weight":[31],"is":[32,100,110],"exactly":[33],"difference":[35],"between":[36],"Wasserstein":[38],"distance":[39],"related":[40],"to":[41,102,154],"two":[42],"probability":[43,51,74,118],"measures":[44,119],"and":[45,129],"certain":[46],"graph":[47],"distance.":[48],"Here,":[49],"measure":[52,141],"may":[53],"be":[54,155],"chosen":[55,121],"[Formula:":[58,65,123,130],"see":[59,66,124,131],"text]-lazy":[60,67,125,132],"one-step":[61,126],"random":[62,69,127,134],"walk,":[63,70,135],"two-step":[68,133],"or":[71],"general":[73],"measure.":[75],"Based":[76],"ODE":[79],"theory,":[80],"show":[82],"that":[83,138],"initial":[85],"value":[86],"problem":[87,104],"has":[88,142],"unique":[90],"global":[91],"solution.":[92],"A":[93],"discrete":[94,115],"version":[95],"above":[98],"applied":[101],"community":[106],"detection.":[107],"Our":[108],"algorithm":[109,164],"based":[111,170],"such":[113],"evolution,":[116],"where":[117],"are":[120],"walk":[128],"respectively.":[136],"Note":[137],"latter":[140],"not":[143],"been":[144],"used":[145],"in":[146],"previous":[147],"works.":[148],"Moreover,":[149],"only":[150],"one":[151],"surgery":[152],"needs":[153],"performed":[156],"after":[157],"last":[159],"iteration,":[160],"which":[161],"makes":[162],"our":[163],"much":[165],"simpler":[166],"than":[167],"earlier":[168],"ones":[169],"Lin\u2013Lu\u2013Yau\u2019s":[172],"curvature.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":3}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2024-11-15T00:00:00"}