{"id":"https://openalex.org/W2886163915","doi":"https://doi.org/10.1093/comjnl/bxz141","title":"Spectra, Hitting Times and Resistance Distances of<i>q</i>- Subdivision Graphs","display_name":"Spectra, Hitting Times and Resistance Distances of<i>q</i>- Subdivision Graphs","publication_year":2019,"publication_date":"2019-10-28","ids":{"openalex":"https://openalex.org/W2886163915","doi":"https://doi.org/10.1093/comjnl/bxz141","mag":"2886163915"},"language":"en","primary_location":{"id":"doi:10.1093/comjnl/bxz141","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxz141","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"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":"The Computer Journal","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.00372","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112320241","display_name":"Yibo Zeng","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yibo Zeng","raw_affiliation_strings":["School of Mathematical Sciences, Fudan University, Shanghai 200433, China","Shanghai Key Laboratory of Intelligent Information, Shanghai 200433, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Fudan University, Shanghai 200433, China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Intelligent Information, Shanghai 200433, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067533846","display_name":"Zhongzhi Zhang","orcid":"https://orcid.org/0000-0003-1260-2079"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhongzhi Zhang","raw_affiliation_strings":["Fudan-Zhongan Joint Laboratory of Blockchain and Information Security, Fudan University, Shanghai, 200433, China","School of Computer Science, Fudan University, Shanghai 200433, China","Shanghai Engineering Research Institute of Blockchain, Fudan University, Shanghai 200433, China","Shanghai Key Laboratory of Intelligent Information, Shanghai 200433, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fudan-Zhongan Joint Laboratory of Blockchain and Information Security, Fudan University, Shanghai, 200433, China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"School of Computer Science, Fudan University, Shanghai 200433, China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Shanghai Engineering Research Institute of Blockchain, Fudan University, Shanghai 200433, China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Intelligent Information, Shanghai 200433, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067533846"],"corresponding_institution_ids":["https://openalex.org/I24943067"],"apc_list":{"value":2635,"currency":"GBP","value_usd":3232},"apc_paid":null,"fwci":0.5554,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.62734918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"64","issue":"1","first_page":"76","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9995999932289124,"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/T11476","display_name":"Graph theory and applications","score":0.9993000030517578,"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":0.9977999925613403,"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/subdivision","display_name":"Subdivision","score":0.792330265045166},{"id":"https://openalex.org/keywords/resistance-distance","display_name":"Resistance distance","score":0.7476170659065247},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.7007918357849121},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6775636076927185},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6159840822219849},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5789754986763},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5776400566101074},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.572615385055542},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.467803031206131},{"id":"https://openalex.org/keywords/hitting-time","display_name":"Hitting time","score":0.4244571924209595},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40310028195381165},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.32001370191574097},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13977941870689392},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.1205706000328064},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07693937420845032}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.792330265045166},{"id":"https://openalex.org/C612898","wikidata":"https://www.wikidata.org/wiki/Q7315618","display_name":"Resistance distance","level":5,"score":0.7476170659065247},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.7007918357849121},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6775636076927185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6159840822219849},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5789754986763},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5776400566101074},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.572615385055542},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.467803031206131},{"id":"https://openalex.org/C199277547","wikidata":"https://www.wikidata.org/wiki/Q5872687","display_name":"Hitting time","level":2,"score":0.4244571924209595},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40310028195381165},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.32001370191574097},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13977941870689392},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.1205706000328064},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07693937420845032},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","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/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/comjnl/bxz141","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxz141","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"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":"The Computer Journal","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1808.00372","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.00372","pdf_url":"https://arxiv.org/pdf/1808.00372","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:1808.00372","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.00372","pdf_url":"https://arxiv.org/pdf/1808.00372","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":[{"id":"https://openalex.org/G2547718675","display_name":null,"funder_award_id":"2018YFB1305104","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G537946182","display_name":null,"funder_award_id":"61872093","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6271259443","display_name":null,"funder_award_id":"2018SHZDZX01","funder_id":"https://openalex.org/F4320321885","funder_display_name":"Science and Technology Commission of Shanghai Municipality"},{"id":"https://openalex.org/G6569941313","display_name":null,"funder_award_id":"61803248","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321885","display_name":"Science and Technology Commission of Shanghai Municipality","ror":"https://ror.org/03kt66j61"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":79,"referenced_works":["https://openalex.org/W1479863711","https://openalex.org/W1578099820","https://openalex.org/W1589331344","https://openalex.org/W1875795917","https://openalex.org/W1907790026","https://openalex.org/W1969888675","https://openalex.org/W1971421925","https://openalex.org/W1972636593","https://openalex.org/W1973353128","https://openalex.org/W1976849572","https://openalex.org/W1984885659","https://openalex.org/W1987401949","https://openalex.org/W1987717935","https://openalex.org/W1998200279","https://openalex.org/W1999028753","https://openalex.org/W2001685082","https://openalex.org/W2005203581","https://openalex.org/W2008620264","https://openalex.org/W2021757174","https://openalex.org/W2021761546","https://openalex.org/W2028836627","https://openalex.org/W2029240401","https://openalex.org/W2039658286","https://openalex.org/W2040871213","https://openalex.org/W2048572907","https://openalex.org/W2053015976","https://openalex.org/W2057084113","https://openalex.org/W2080478510","https://openalex.org/W2081084405","https://openalex.org/W2088012076","https://openalex.org/W2090247235","https://openalex.org/W2090463147","https://openalex.org/W2103132901","https://openalex.org/W2112090702","https://openalex.org/W2112147870","https://openalex.org/W2112681514","https://openalex.org/W2123196001","https://openalex.org/W2136647665","https://openalex.org/W2148606196","https://openalex.org/W2153624566","https://openalex.org/W2160058983","https://openalex.org/W2160321012","https://openalex.org/W2167064216","https://openalex.org/W2172067437","https://openalex.org/W2193378305","https://openalex.org/W2213736476","https://openalex.org/W2259770190","https://openalex.org/W2266714125","https://openalex.org/W2323784209","https://openalex.org/W2478475484","https://openalex.org/W2533564839","https://openalex.org/W2592053950","https://openalex.org/W2595972220","https://openalex.org/W2748196059","https://openalex.org/W2752776682","https://openalex.org/W2947171186","https://openalex.org/W2963181629","https://openalex.org/W2963287098","https://openalex.org/W2963308324","https://openalex.org/W2963995521","https://openalex.org/W2964119693","https://openalex.org/W3004555699","https://openalex.org/W3101505259","https://openalex.org/W3101649852","https://openalex.org/W3102629426","https://openalex.org/W3102915455","https://openalex.org/W3104559337","https://openalex.org/W3105775578","https://openalex.org/W3121639809","https://openalex.org/W3141776272","https://openalex.org/W4247782380","https://openalex.org/W4250466849","https://openalex.org/W4300190926","https://openalex.org/W6639440540","https://openalex.org/W6640041125","https://openalex.org/W6643390548","https://openalex.org/W6677111876","https://openalex.org/W6686994558","https://openalex.org/W6742756875"],"related_works":["https://openalex.org/W3034120174","https://openalex.org/W3120733914","https://openalex.org/W2766073208","https://openalex.org/W1974398340","https://openalex.org/W2884767994","https://openalex.org/W2001241184","https://openalex.org/W2962778578","https://openalex.org/W4299580042","https://openalex.org/W4385981789","https://openalex.org/W2346372059"],"abstract_inverted_index":{"Abstract":[0],"Subdivision,":[1],"triangulation,":[2],"Kronecker":[3],"product,":[4],"corona":[5],"product":[6],"and":[7,72,96,115],"many":[8,82],"other":[9],"graph":[10,43,47],"operations":[11],"or":[12],"products":[13],"play":[14],"an":[15],"important":[16],"role":[17],"in":[18,58,86],"complex":[19,37],"networks.":[20,38,151],"In":[21],"this":[22],"paper,":[23],"we":[24,132],"study":[25,121],"the":[26,94,122,125,134],"properties":[27,123],"of":[28,64,84,88,98,124,140],"$q$-subdivision":[29,46,127],"graphs,":[30,128],"which":[31,131,143],"have":[32],"been":[33,145],"applied":[34],"to":[35,91,147],"model":[36],"For":[39],"a":[40,138],"simple":[41],"connected":[42],"$G$,":[44,92],"its":[45,75],"$S_q(G)$":[48,85],"is":[49],"obtained":[50],"from":[51],"$G$":[52,59],"through":[53],"replacing":[54],"every":[55],"edge":[56],"$uv$":[57],"by":[60],"$q$":[61],"disjoint":[62],"paths":[63],"length":[65],"2,":[66],"with":[67],"each":[68],"path":[69],"having":[70],"$u$":[71],"$v$":[73],"as":[74],"ends.":[76],"We":[77,119],"derive":[78],"explicit":[79],"formulas":[80],"for":[81,137],"quantities":[83],"terms":[87],"those":[89],"corresponding":[90],"including":[93],"eigenvalues":[95],"eigenvectors":[97],"normalized":[99],"adjacency":[100],"matrix,":[101],"two-node":[102,107],"hitting":[103],"time,":[104],"Kemeny":[105],"constant,":[106],"resistance":[108],"distance,":[109],"Kirchhoff":[110],"index,":[111],"additive":[112],"degree-Kirchhoff":[113,117],"index":[114],"multiplicative":[116],"index.":[118],"also":[120],"iterated":[126],"based":[129],"on":[130],"obtain":[133],"closed-form":[135],"expressions":[136],"family":[139],"hierarchical":[141],"lattices,":[142],"has":[144],"used":[146],"describe":[148],"scale-free":[149],"fractal":[150]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2018-08-22T00:00:00"}