{"id":"https://openalex.org/W2904221347","doi":"https://doi.org/10.20382/jocg.v10i1a16","title":"The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs","display_name":"The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs","publication_year":2018,"publication_date":"2018-12-13","ids":{"openalex":"https://openalex.org/W2904221347","doi":"https://doi.org/10.20382/jocg.v10i1a16","mag":"2904221347"},"language":"en","primary_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/3082","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3082","pdf_url":"https://jocg.org/index.php/jocg/article/view/3082","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 10 No. 1 (2019); 477\u2013499","raw_type":"info:eu-repo/semantics/article"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://jocg.org/index.php/jocg/article/view/3082","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027360301","display_name":"Ellen Gasparovic","orcid":"https://orcid.org/0000-0003-3775-9785"},"institutions":[{"id":"https://openalex.org/I177328695","display_name":"Union College","ror":"https://ror.org/058w5nk68","country_code":"US","type":"education","lineage":["https://openalex.org/I177328695"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gasparovic, Ellen","raw_affiliation_strings":["*Union College"],"affiliations":[{"raw_affiliation_string":"*Union College","institution_ids":["https://openalex.org/I177328695"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013231102","display_name":"Maria Gommel","orcid":null},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gommel, Maria","raw_affiliation_strings":["University of Iowa"],"affiliations":[{"raw_affiliation_string":"University of Iowa","institution_ids":["https://openalex.org/I126307644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022505886","display_name":"Emilie Purvine","orcid":"https://orcid.org/0000-0003-2069-5594"},"institutions":[{"id":"https://openalex.org/I142606810","display_name":"Pacific Northwest National Laboratory","ror":"https://ror.org/05h992307","country_code":"US","type":"facility","lineage":["https://openalex.org/I1325736334","https://openalex.org/I1330989302","https://openalex.org/I142606810","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Purvine, Emilie","raw_affiliation_strings":["Pacific Northwest National Laboratory,"],"affiliations":[{"raw_affiliation_string":"Pacific Northwest National Laboratory,","institution_ids":["https://openalex.org/I142606810"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039716567","display_name":"Radmila Sazdanovi\u0107","orcid":"https://orcid.org/0000-0003-1321-1651"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sazdanovic, Radmila","raw_affiliation_strings":["North Carolina State University ,"],"affiliations":[{"raw_affiliation_string":"North Carolina State University ,","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100349956","display_name":"Bei Wang","orcid":"https://orcid.org/0000-0002-9240-0700"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Bei","raw_affiliation_strings":["University of Utah"],"affiliations":[{"raw_affiliation_string":"University of Utah","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101536052","display_name":"Yusu Wang","orcid":"https://orcid.org/0000-0001-7950-4348"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Yusu","raw_affiliation_strings":["Ohio State University"],"affiliations":[{"raw_affiliation_string":"Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043121321","display_name":"Lori Ziegelmeier","orcid":"https://orcid.org/0000-0002-1544-4937"},"institutions":[{"id":"https://openalex.org/I5444425","display_name":"Macalester College","ror":"https://ror.org/04fceqm38","country_code":"US","type":"education","lineage":["https://openalex.org/I5444425"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ziegelmeier, Lori","raw_affiliation_strings":["Macalester College ,"],"affiliations":[{"raw_affiliation_string":"Macalester College ,","institution_ids":["https://openalex.org/I5444425"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5027360301"],"corresponding_institution_ids":["https://openalex.org/I177328695"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1951568,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.9998000264167786,"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":0.9998000264167786,"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"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9800999760627747,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T13282","display_name":"Automated Road and Building Extraction","score":0.9753000140190125,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7513521313667297},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.5093032121658325},{"id":"https://openalex.org/keywords/metric-dimension","display_name":"Metric dimension","score":0.4889337122440338},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.47701048851013184},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.47318172454833984},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.45711684226989746},{"id":"https://openalex.org/keywords/distance","display_name":"Distance","score":0.4532930552959442},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45068731904029846},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.42946162819862366},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3622308373451233},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3373386859893799},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3334307372570038},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1833760142326355},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.17045918107032776},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.0915011465549469},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.08931884169578552}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7513521313667297},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5093032121658325},{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.4889337122440338},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.47701048851013184},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.47318172454833984},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.45711684226989746},{"id":"https://openalex.org/C54385418","wikidata":"https://www.wikidata.org/wiki/Q2742711","display_name":"Distance","level":4,"score":0.4532930552959442},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45068731904029846},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.42946162819862366},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3622308373451233},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3373386859893799},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3334307372570038},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1833760142326355},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.17045918107032776},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0915011465549469},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.08931884169578552},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:ojs.library.carleton.ca:article/3082","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3082","pdf_url":"https://jocg.org/index.php/jocg/article/view/3082","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 10 No. 1 (2019); 477\u2013499","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:1812.05282","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.05282","pdf_url":"https://arxiv.org/pdf/1812.05282","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"},{"id":"mag:2904221347","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1812.05282.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1812.05282","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1812.05282","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"},{"id":"doi:10.20382/jocg.v10i1a16","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v10i1a16","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"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-journal"}],"best_oa_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/3082","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3082","pdf_url":"https://jocg.org/index.php/jocg/article/view/3082","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 10 No. 1 (2019); 477\u2013499","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.7699999809265137,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1302751805","display_name":"RI: Small: Learning discrete structure from continuous spaces","funder_award_id":"1815697","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1899721271","display_name":null,"funder_award_id":"AC05-76RL01830","funder_id":"https://openalex.org/F4320306250","funder_display_name":"Battelle"},{"id":"https://openalex.org/G1967746503","display_name":null,"funder_award_id":"DE-AC05-76RL01830","funder_id":"https://openalex.org/F4320338354","funder_display_name":"Pacific Northwest National Laboratory"},{"id":"https://openalex.org/G2137412393","display_name":null,"funder_award_id":"DMS-1547357","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2506945562","display_name":null,"funder_award_id":"76RL01830","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2510423872","display_name":null,"funder_award_id":"AC05-76RL01830","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3187039853","display_name":null,"funder_award_id":"RI-1815697","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3207167323","display_name":null,"funder_award_id":"DBI-1661375","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4229663209","display_name":null,"funder_award_id":"1547357","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4422678049","display_name":"Collaborative Research: CDS&E-MSS: Exact Homological Algebra for Computational Topology","funder_award_id":"1854703","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5200347334","display_name":null,"funder_award_id":"DE-AC05-76RL01830","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5269527469","display_name":null,"funder_award_id":"DE-AC05-76RL0","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5321382714","display_name":null,"funder_award_id":"76RL01830","funder_id":"https://openalex.org/F4320338354","funder_display_name":"Pacific Northwest National Laboratory"},{"id":"https://openalex.org/G5726405315","display_name":null,"funder_award_id":"DE-AC05","funder_id":"https://openalex.org/F4320306250","funder_display_name":"Battelle"},{"id":"https://openalex.org/G5923273611","display_name":null,"funder_award_id":"IIS-1513616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6099464845","display_name":"III: Medium: Collaborative Research: Topological Data Analysis for Large Network Visualization","funder_award_id":"1513616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6358103127","display_name":null,"funder_award_id":"DMS-1854705","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6367296400","display_name":null,"funder_award_id":"1740761","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6664334341","display_name":null,"funder_award_id":"DE-AC05-76RL01830","funder_id":"https://openalex.org/F4320306250","funder_display_name":"Battelle"},{"id":"https://openalex.org/G7200503492","display_name":null,"funder_award_id":"DE-AC05-76RL01830","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7560550554","display_name":null,"funder_award_id":"76RL01830","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7649787314","display_name":"Collaborative Research: ABI Innovation: A Scalable Framework for Visual Exploration and Hypotheses Extraction of Phenomics Data using Topological Analytics","funder_award_id":"1661375","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7995982022","display_name":null,"funder_award_id":"DE-AC05","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8053250311","display_name":null,"funder_award_id":"SQuaRE","funder_id":"https://openalex.org/F4320307521","funder_display_name":"American Institute of Mathematics"},{"id":"https://openalex.org/G8236974595","display_name":null,"funder_award_id":"DE-AC05-76RL0183","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8277545319","display_name":null,"funder_award_id":"DE-AC05-76RL01830.","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G829320215","display_name":"Workshop for Women in Computational Topology","funder_award_id":"1619908","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8414908677","display_name":null,"funder_award_id":"DE-AC0","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8717196466","display_name":"Collaborative Research: Computational Topology and Categorification of Cancer Genomic Data: Theory and Algorithms","funder_award_id":"1854705","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G998451652","display_name":null,"funder_award_id":"DE-AC05-76RL01830.","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306250","display_name":"Battelle","ror":"https://ror.org/01h5tnr73"},{"id":"https://openalex.org/F4320307521","display_name":"American Institute of Mathematics","ror":"https://ror.org/02a0fwv66"},{"id":"https://openalex.org/F4320338354","display_name":"Pacific Northwest National Laboratory","ror":"https://ror.org/05h992307"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2904221347.pdf","grobid_xml":"https://content.openalex.org/works/W2904221347.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1511069251","https://openalex.org/W1581051117","https://openalex.org/W1607787316","https://openalex.org/W1991566301","https://openalex.org/W2032338144","https://openalex.org/W2108182844","https://openalex.org/W2144572173","https://openalex.org/W2161184224","https://openalex.org/W2190928263","https://openalex.org/W2592389402","https://openalex.org/W2807222275","https://openalex.org/W2890370060","https://openalex.org/W2900506937","https://openalex.org/W2962902468","https://openalex.org/W2963212950","https://openalex.org/W3040586665","https://openalex.org/W3101063812"],"related_works":["https://openalex.org/W3046423622","https://openalex.org/W2963378502","https://openalex.org/W2962973811","https://openalex.org/W2151469863","https://openalex.org/W3200249410","https://openalex.org/W2154136271","https://openalex.org/W1830894108","https://openalex.org/W3007089961","https://openalex.org/W3101063812","https://openalex.org/W2124218764","https://openalex.org/W3046604617","https://openalex.org/W2782043804","https://openalex.org/W3163505644","https://openalex.org/W2561245576","https://openalex.org/W2090996403","https://openalex.org/W1581489722","https://openalex.org/W3100616040","https://openalex.org/W1676815674","https://openalex.org/W3125201685","https://openalex.org/W2027117212"],"abstract_inverted_index":{"Metric":[0],"graphs":[1,33,82,117,133],"are":[2,40,134],"meaningful":[3],"objects":[4],"for":[5,93],"modeling":[6],"complex":[7],"structures":[8,27],"that":[9],"arise":[10],"in":[11,28,34,42,110],"many":[12],"real-world":[13],"applications,":[14],"such":[15],"as":[16],"road":[17],"networks,":[18],"river":[19],"systems,":[20],"earthquake":[21],"faults,":[22],"blood":[23],"vessels,":[24],"and":[25,64,106,122,141],"filamentary":[26],"galaxies.":[29],"To":[30],"study":[31],"metric":[32,58,81],"the":[35,44,60,65,75,88,94,103,111,116,123],"context":[36],"of":[37,48,55,87,91,115,139],"comparison,":[38],"we":[39],"interested":[41],"determining":[43],"relative":[45],"discriminative":[46],"capabilities":[47],"two":[49,80],"topology-based":[50],"distances":[51,109],"between":[52,79,102],"a":[53,119],"pair":[54],"arbitrary":[56],"finite":[57],"graphs:":[59],"persistence":[61,107],"distortion":[62,108],"distance":[63,78],"intrinsic":[66,76,104],"Cech":[67,77,105],"distance.":[68],"We":[69],"explicitly":[70],"show":[71],"how":[72],"to":[73],"compute":[74],"based":[83],"solely":[84],"on":[85],"knowledge":[86],"shortest":[89],"systems":[90],"loops":[92],"graphs.":[95],"Our":[96],"main":[97],"theorem":[98],"establishes":[99],"an":[100],"inequality":[101],"case":[112],"when":[113,131],"one":[114],"is":[118,125],"bouquet":[120],"graph":[121],"other":[124],"arbitrary.":[126],"The":[127],"relationship":[128],"also":[129],"holds":[130],"both":[132],"constructed":[135],"via":[136],"wedge":[137],"sums":[138],"cycles":[140],"edges.":[142]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}