{"id":"https://openalex.org/W2915949412","doi":"https://doi.org/10.1093/comnet/cnz005","title":"Transfinite fractal dimension of trees and hierarchical scale-free graphs","display_name":"Transfinite fractal dimension of trees and hierarchical scale-free graphs","publication_year":2019,"publication_date":"2019-01-23","ids":{"openalex":"https://openalex.org/W2915949412","doi":"https://doi.org/10.1093/comnet/cnz005","mag":"2915949412"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnz005","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnz005","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.02674","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"J\u00falia Komj\u00e1thy","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"J\u00falia Komj\u00e1thy","raw_affiliation_strings":["Department of Mathematics and Computer Science, Eindhoven University of Technology, MB Eindhoven, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Eindhoven University of Technology, MB Eindhoven, Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Roland Molontay","orcid":null},"institutions":[{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Roland Molontay","raw_affiliation_strings":["Department of Stochastics, Budapest University of Technology and Economics, 1521 Budapest, Hungary and MTA-BME Stochastics Research Group, 1521 Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Stochastics, Budapest University of Technology and Economics, 1521 Budapest, Hungary and MTA-BME Stochastics Research Group, 1521 Budapest, Hungary","institution_ids":["https://openalex.org/I29770179"]}]},{"author_position":"last","author":{"id":null,"display_name":"K\u00e1roly Simon","orcid":null},"institutions":[{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"K\u00e1roly Simon","raw_affiliation_strings":["Department of Stochastics, Budapest University of Technology and Economics, 1521 Budapest, Hungary and MTA-BME Stochastics Research Group, 1521 Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Stochastics, Budapest University of Technology and Economics, 1521 Budapest, Hungary and MTA-BME Stochastics Research Group, 1521 Budapest, Hungary","institution_ids":["https://openalex.org/I29770179"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I29770179"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.7706,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73271013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":"5","first_page":"764","last_page":"791"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.21780000627040863,"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":0.21780000627040863,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.2160000056028366,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.18930000066757202,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.9588000178337097},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.6700000166893005},{"id":"https://openalex.org/keywords/fractal-dimension-on-networks","display_name":"Fractal dimension on networks","score":0.6581000089645386},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.6571999788284302},{"id":"https://openalex.org/keywords/minkowski\u2013bouligand-dimension","display_name":"Minkowski\u2013Bouligand dimension","score":0.5756000280380249},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.53329998254776},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.46480000019073486},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44839999079704285}],"concepts":[{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.9588000178337097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7233999967575073},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.6700000166893005},{"id":"https://openalex.org/C60396315","wikidata":"https://www.wikidata.org/wiki/Q5477489","display_name":"Fractal dimension on networks","level":5,"score":0.6581000089645386},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.6571999788284302},{"id":"https://openalex.org/C101597101","wikidata":"https://www.wikidata.org/wiki/Q2555655","display_name":"Minkowski\u2013Bouligand dimension","level":4,"score":0.5756000280380249},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.53329998254776},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.46480000019073486},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44839999079704285},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4408000111579895},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.4147999882698059},{"id":"https://openalex.org/C96175551","wikidata":"https://www.wikidata.org/wiki/Q3100949","display_name":"Fractal landscape","level":5,"score":0.3939000070095062},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.37950000166893005},{"id":"https://openalex.org/C83764196","wikidata":"https://www.wikidata.org/wiki/Q17014577","display_name":"Fractal derivative","level":5,"score":0.3328000009059906},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31929999589920044},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/comnet/cnz005","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnz005","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex Networks","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1808.02674","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.02674","pdf_url":"https://arxiv.org/pdf/1808.02674","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1808.02674","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.02674","pdf_url":"https://arxiv.org/pdf/1808.02674","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"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W121824094","https://openalex.org/W1973353128","https://openalex.org/W1980785259","https://openalex.org/W1982573076","https://openalex.org/W1992611645","https://openalex.org/W1993324602","https://openalex.org/W2006276645","https://openalex.org/W2008437427","https://openalex.org/W2008620264","https://openalex.org/W2017264826","https://openalex.org/W2018049970","https://openalex.org/W2037178802","https://openalex.org/W2040871213","https://openalex.org/W2044881936","https://openalex.org/W2049194621","https://openalex.org/W2053015976","https://openalex.org/W2059405458","https://openalex.org/W2080478510","https://openalex.org/W2082017510","https://openalex.org/W2084504453","https://openalex.org/W2112976607","https://openalex.org/W2139087731","https://openalex.org/W2160058983","https://openalex.org/W2205000987","https://openalex.org/W2343433175","https://openalex.org/W2587523352","https://openalex.org/W2806863676","https://openalex.org/W4301357400","https://openalex.org/W6727427139","https://openalex.org/W6752826495","https://openalex.org/W6753856429"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,91],"article,":[3],"we":[4,52,120],"introduce":[5,111],"a":[6,64,82],"new":[7],"concept:":[8],"the":[9,18,33,55,70,75,78,96,104,112,122,132],"transfinite":[10,113,126],"fractal":[11,58,79,115,127],"dimension":[12,59,80,108,128],"of":[13,20,22,35,49,57,85,99,106,129],"graph":[14,86,134],"sequences":[15],"motivated":[16],"by":[17,26,138],"notion":[19],"fractality":[21,36],"complex":[23],"networks":[24,41],"proposed":[25],"Song":[27],"et":[28],"al.":[29],"We":[30,88,101],"show":[31,53],"that":[32,54,66,90],"definition":[34,56],"cannot":[37],"be":[38,61],"applied":[39],"to":[40,95],"with":[42,74],"\u2018tree-like\u2019":[43],"structure":[44],"and":[45,73,110,125,140,147],"exponential":[46,71],"growth":[47,97],"rate":[48,98],"neighbourhoods.":[50],"However,":[51],"could":[60],"modified":[62,76],"in":[63],"way":[65],"takes":[67],"into":[68],"account":[69],"growth,":[72],"definition,":[77],"becomes":[81],"proper":[83],"parameter":[84,92],"sequences.":[87],"find":[89],"is":[93],"related":[94],"trees.":[100,150],"also":[102],"generalize":[103],"concept":[105],"box":[107],"further":[109],"Cesaro":[114],"dimension.":[116],"Using":[117],"rigorous":[118],"proofs,":[119],"determine":[121],"optimal":[123],"box-covering":[124],"various":[130],"models:":[131],"hierarchical":[133],"sequence":[135],"model":[136],"introduced":[137],"Komj\u00e1thy":[139],"Simon,":[141],"Song\u2013Havlin\u2013Makse":[142],"model,":[143],"spherically":[144],"symmetric":[145],"trees":[146],"supercritical":[148],"Galton\u2013Watson":[149]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2019-03-02T00:00:00"}