{"id":"https://openalex.org/W1906044051","doi":"https://doi.org/10.37236/5909","title":"Edge Reconstruction of the Ihara Zeta Function","display_name":"Edge Reconstruction of the Ihara Zeta Function","publication_year":2018,"publication_date":"2018-05-11","ids":{"openalex":"https://openalex.org/W1906044051","doi":"https://doi.org/10.37236/5909","mag":"1906044051"},"language":"en","primary_location":{"id":"doi:10.37236/5909","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5909","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/5909","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044563946","display_name":"Gunther Cornelissen","orcid":"https://orcid.org/0000-0003-3787-2550"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Gunther Cornelissen","raw_affiliation_strings":["Mathematisch instituut, Universiteit Utrecht, Nederland"],"affiliations":[{"raw_affiliation_string":"Mathematisch instituut, Universiteit Utrecht, Nederland","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084322976","display_name":"Janne Kool","orcid":null},"institutions":[{"id":"https://openalex.org/I4210130413","display_name":"McDonald's (United States)","ror":"https://ror.org/03t0k7069","country_code":"US","type":"company","lineage":["https://openalex.org/I4210130413"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Janne Kool","raw_affiliation_strings":["Kognitive Systemer\r\n DTU Compute\r\nDansk Tekniske Universitet \r\nDanmark","with an appendix by Daniel McDonald"],"affiliations":[{"raw_affiliation_string":"Kognitive Systemer\r\n DTU Compute\r\nDansk Tekniske Universitet \r\nDanmark","institution_ids":[]},{"raw_affiliation_string":"with an appendix by Daniel McDonald","institution_ids":["https://openalex.org/I4210130413"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044563946"],"corresponding_institution_ids":["https://openalex.org/I193662353"],"apc_list":null,"apc_paid":null,"fwci":0.3861,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52516364,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9983999729156494,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/mathematics","display_name":"Mathematics","score":0.7648653984069824},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.687588632106781},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6506937742233276},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.5972154140472412},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.5749157667160034},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5622286200523376},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4541269838809967},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4459465742111206},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.444613516330719},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39789021015167236},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2616112232208252},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07324591279029846}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7648653984069824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.687588632106781},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6506937742233276},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.5972154140472412},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.5749157667160034},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5622286200523376},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4541269838809967},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4459465742111206},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.444613516330719},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39789021015167236},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2616112232208252},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07324591279029846},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.37236/5909","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5909","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1507.03411","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.03411","pdf_url":"https://arxiv.org/pdf/1507.03411","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":"","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:742929","is_oa":false,"landing_page_url":"http://edoc.mpg.de/742929","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":"Electronic Journal of Combinatorics, v.25 (2018)","raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:publications/a3e1f9f1-630a-43ee-bb96-e67e5abad9b9","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/a3e1f9f1-630a-43ee-bb96-e67e5abad9b9","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cornelissen , G & Kool , J 2018 , ' Edge reconstruction of the Ihara zeta function ' , The Electronic Journal of Combinatorics , vol. 25 , no. 2 , P2.26 .","raw_type":"article"},{"id":"pmh:oai:pure.mpg.de:item_3117816","is_oa":true,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0004-069D-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Combinatorics","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/375342","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/375342","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Combinatorics, 25(2). Electronic Journal of Combinatorics","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1507.03411","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1507.03411","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":"mag:1906044051","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/5909","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5909","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320279","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86"},{"id":"https://openalex.org/F4320328568","display_name":"Hausdorff Center for Mathematics","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1487444668","https://openalex.org/W1515697879","https://openalex.org/W2001194443","https://openalex.org/W2003824380","https://openalex.org/W2005975683","https://openalex.org/W2024514015","https://openalex.org/W2040590647","https://openalex.org/W2082397064","https://openalex.org/W2091203438","https://openalex.org/W2100454584","https://openalex.org/W2120567229","https://openalex.org/W2142193905","https://openalex.org/W2253653959","https://openalex.org/W2323143735"],"related_works":["https://openalex.org/W2962834114","https://openalex.org/W1564712708","https://openalex.org/W2950994095","https://openalex.org/W2253653959","https://openalex.org/W2416403931","https://openalex.org/W3186482404","https://openalex.org/W2009358426","https://openalex.org/W171239498","https://openalex.org/W2057196428","https://openalex.org/W2790609319","https://openalex.org/W598746159","https://openalex.org/W2988039487","https://openalex.org/W2768440044","https://openalex.org/W1668045384","https://openalex.org/W2999918261","https://openalex.org/W2884317413","https://openalex.org/W2562050321","https://openalex.org/W3188181493","https://openalex.org/W2962985657","https://openalex.org/W2143968888"],"abstract_inverted_index":{"We":[0,23,57],"show":[1],"that":[2,59,62,96],"if":[3,63],"a":[4,44,78,87,99],"graph":[5],"$G$":[6,20],"has":[7,43],"average":[8],"degree":[9],"$\\overline":[10,64],"d":[11],"\\geq":[12],"4$,":[13],"then":[14],"the":[15,30,69,81,93],"Ihara":[16],"zeta":[17],"function":[18],"of":[19,29,71,84],"is":[21,36],"edge-reconstructible.":[22],"prove":[24,58],"some":[25],"general":[26],"spectral":[27],"properties":[28],"edge":[31,101],"adjacency":[32],"operator":[33],"$T$:":[34],"it":[35,49],"symmetric":[37],"for":[38],"an":[39],"indefinite":[40],"form":[41],"and":[42],"\"large\"":[45],"semi-simple":[46,54],"part":[47],"(but":[48],"can":[50,67],"fail":[51],"to":[52],"be":[53],"in":[55,102],"general).":[56],"this":[60],"implies":[61],"d>4$,":[65],"one":[66],"reconstruct":[68],"number":[70],"non-backtracking":[72],"(closed":[73],"or":[74],"not)":[75],"walks":[76,95],"through":[77,98],"given":[79,100],"edge,":[80],"Perron-Frobenius":[82],"eigenvector":[83],"$T$":[85],"(modulo":[86],"natural":[88],"symmetry),":[89],"as":[90,92],"well":[91],"closed":[94],"pass":[97],"both":[103],"directions":[104],"at":[105],"least":[106],"once.":[107]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}