{"id":"https://openalex.org/W4406191719","doi":"https://doi.org/10.48550/arxiv.2501.03553","title":"Persistent Homology with Path-Representable Distances on Graph Data","display_name":"Persistent Homology with Path-Representable Distances on Graph Data","publication_year":2025,"publication_date":"2025-01-07","ids":{"openalex":"https://openalex.org/W4406191719","doi":"https://doi.org/10.48550/arxiv.2501.03553"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2501.03553","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.03553","pdf_url":"https://arxiv.org/pdf/2501.03553","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2501.03553","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113189047","display_name":"Eunwoo Heo","orcid":"https://orcid.org/0009-0004-3886-1276"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Heo, Eunwoo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069338437","display_name":"Byeong Yeob Choi","orcid":"https://orcid.org/0000-0002-4205-1442"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Choi, Byeongchan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102012499","display_name":"Jae-Hun Jung","orcid":"https://orcid.org/0000-0001-7923-0674"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jung, Jae-Hun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9984999895095825,"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/path","display_name":"Path (computing)","score":0.6102339029312134},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5650317668914795},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.5598926544189453},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.5207028985023499},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4512655735015869},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3637051582336426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35006439685821533},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.329231858253479},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.3034610152244568},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.2780683636665344},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17745494842529297},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.11383041739463806},{"id":"https://openalex.org/keywords/gene","display_name":"Gene","score":0.08982369303703308}],"concepts":[{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6102339029312134},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5650317668914795},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.5598926544189453},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.5207028985023499},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4512655735015869},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3637051582336426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35006439685821533},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.329231858253479},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.3034610152244568},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.2780683636665344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17745494842529297},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.11383041739463806},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.08982369303703308}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2501.03553","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.03553","pdf_url":"https://arxiv.org/pdf/2501.03553","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2501.03553","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2501.03553","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2501.03553","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2501.03553","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.03553","pdf_url":"https://arxiv.org/pdf/2501.03553","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G294838737","display_name":null,"funder_award_id":"2021R1A2C3009648","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G4839914417","display_name":null,"funder_award_id":"2018R1D1A1A02086097","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G5189698939","display_name":null,"funder_award_id":"2021R1A2C3009648","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406191719.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2958601279","https://openalex.org/W2102692026","https://openalex.org/W4360887047","https://openalex.org/W3162517897","https://openalex.org/W2770791287","https://openalex.org/W3143913977","https://openalex.org/W4206186921","https://openalex.org/W4386755584","https://openalex.org/W4289362969","https://openalex.org/W2745914844"],"abstract_inverted_index":{"Persistent":[0],"homology":[1],"(PH)":[2],"has":[3,17],"been":[4,18],"widely":[5],"applied":[6,200],"to":[7,10,20,106,167,195,201],"graph":[8,27,75,192],"data":[9],"extract":[11],"topological":[12,133],"features.":[13],"However,":[14],"little":[15],"attention":[16],"paid":[19],"how":[21],"different":[22],"distance":[23,157],"functions":[24,158],"on":[25,45,94,144],"a":[26,41,63,95,131,145,150,160],"affect":[28],"the":[29,67,77,126,156,165,168,184,202],"resulting":[30],"persistence":[31,128],"barcodes":[32,69],"and":[33,50,79,110,163,180,186],"their":[34,55],"interpretations.":[35],"In":[36,59],"this":[37],"paper,":[38],"we":[39,61,97,113,124],"define":[40],"class":[42],"of":[43],"distances":[44,143],"graphs,":[46],"called":[47],"path-representable":[48],"distances,":[49],"investigate":[51],"structural":[52],"relationships":[53,122],"between":[54,66,138],"induced":[56,70,140],"persistent":[57],"homologies.":[58],"particular,":[60],"identify":[62],"nontrivial":[64],"injection":[65,102],"1-dimensional":[68],"by":[71,141],"two":[72],"commonly":[73],"used":[74],"distances:":[76],"unweighted":[78],"weighted":[80],"shortest-path":[81],"distances.":[82,100],"We":[83,148],"formally":[84],"establish":[85],"sufficient":[86],"conditions":[87],"under":[88],"which":[89],"such":[90],"embeddings":[91],"arise,":[92],"focusing":[93],"subclass":[96],"call":[98],"cost-dominated":[99,142],"The":[101],"property":[103],"is":[104],"shown":[105],"hold":[107],"in":[108,183],"0-":[109],"1-dimensions,":[111],"while":[112],"provide":[114],"counterexamples":[115],"for":[116,153],"higher-dimensional":[117],"cases.":[118],"To":[119],"make":[120],"these":[121],"measurable,":[123],"introduce":[125],"total":[127],"difference":[129],"(TPD),":[130],"new":[132],"measure":[134,199],"that":[135],"quantifies":[136],"changes":[137],"filtrations":[139],"fixed":[146],"graph.":[147],"prove":[149],"stability":[151],"result":[152],"TPD":[154,175],"when":[155],"admit":[159],"partial":[161],"order":[162],"apply":[164],"method":[166],"SNAP":[169],"EU":[170],"Research":[171],"Institution":[172],"E-Mail":[173],"dataset.":[174,204],"captures":[176],"both":[177],"periodic":[178],"patterns":[179],"global":[181],"trends":[182],"data,":[185],"shows":[187],"stronger":[188],"alignment":[189],"with":[190],"classical":[191],"statistics":[193],"compared":[194],"an":[196],"existing":[197],"PH-based":[198],"same":[203]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
