{"id":"https://openalex.org/W4221131015","doi":"https://doi.org/10.3390/e24030409","title":"The Structure and First-Passage Properties of Generalized Weighted Koch Networks","display_name":"The Structure and First-Passage Properties of Generalized Weighted Koch Networks","publication_year":2022,"publication_date":"2022-03-15","ids":{"openalex":"https://openalex.org/W4221131015","doi":"https://doi.org/10.3390/e24030409","pmid":"https://pubmed.ncbi.nlm.nih.gov/35327920"},"language":"en","primary_location":{"id":"doi:10.3390/e24030409","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030409","pdf_url":"https://www.mdpi.com/1099-4300/24/3/409/pdf?version=1647331197","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/3/409/pdf?version=1647331197","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000386087","display_name":"Jing Su","orcid":"https://orcid.org/0000-0002-9071-5725"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Su","raw_affiliation_strings":["Key Laboratory of High Confidence Software Technologies, Peking University, Beijing 100871, China","School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China"],"raw_orcid":"https://orcid.org/0000-0002-9071-5725","affiliations":[{"raw_affiliation_string":"Key Laboratory of High Confidence Software Technologies, Peking University, Beijing 100871, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108229342","display_name":"Mingjun Zhang","orcid":"https://orcid.org/0000-0002-5529-1349"},"institutions":[{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mingjun Zhang","raw_affiliation_strings":["China Northwest Center of Financial Research, Lanzhou University of Finance and Economics, Lanzhou 730020, China","Key Laboratory of E-Business Technology and Application, Lanzhou 730020, China","School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Northwest Center of Financial Research, Lanzhou University of Finance and Economics, Lanzhou 730020, China","institution_ids":["https://openalex.org/I4210152533"]},{"raw_affiliation_string":"Key Laboratory of E-Business Technology and Application, Lanzhou 730020, China","institution_ids":[]},{"raw_affiliation_string":"School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, China","institution_ids":["https://openalex.org/I4210152533"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101729321","display_name":"Bing Yao","orcid":"https://orcid.org/0000-0002-5416-5180"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bing Yao","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China","institution_ids":["https://openalex.org/I68986083"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108229342"],"corresponding_institution_ids":["https://openalex.org/I4210152533"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2501,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48613402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"24","issue":"3","first_page":"409","last_page":"409"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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":0.991100013256073,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/clustering-coefficient","display_name":"Clustering coefficient","score":0.7549338340759277},{"id":"https://openalex.org/keywords/weighted-network","display_name":"Weighted network","score":0.7278951406478882},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7023482322692871},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.4991021156311035},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4961291253566742},{"id":"https://openalex.org/keywords/average-path-length","display_name":"Average path length","score":0.4814671576023102},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.47262808680534363},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.45486658811569214},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.44720590114593506},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4296623468399048},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.41942405700683594},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3859363794326782},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.38247138261795044},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3390140235424042},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.3138032555580139},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16249346733093262}],"concepts":[{"id":"https://openalex.org/C22047676","wikidata":"https://www.wikidata.org/wiki/Q898680","display_name":"Clustering coefficient","level":3,"score":0.7549338340759277},{"id":"https://openalex.org/C142323842","wikidata":"https://www.wikidata.org/wiki/Q7979900","display_name":"Weighted network","level":3,"score":0.7278951406478882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7023482322692871},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.4991021156311035},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4961291253566742},{"id":"https://openalex.org/C91886571","wikidata":"https://www.wikidata.org/wiki/Q432520","display_name":"Average path length","level":4,"score":0.4814671576023102},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.47262808680534363},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.45486658811569214},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.44720590114593506},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4296623468399048},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.41942405700683594},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3859363794326782},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.38247138261795044},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3390140235424042},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.3138032555580139},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16249346733093262},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24030409","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030409","pdf_url":"https://www.mdpi.com/1099-4300/24/3/409/pdf?version=1647331197","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:35327920","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35327920","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:32e054c39ff44d00ae995ab79ef1dff6","is_oa":true,"landing_page_url":"https://doaj.org/article/32e054c39ff44d00ae995ab79ef1dff6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 3, p 409 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/3/409/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24030409","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 3; Pages: 409","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8953160","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8953160","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24030409","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030409","pdf_url":"https://www.mdpi.com/1099-4300/24/3/409/pdf?version=1647331197","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3669156218","display_name":null,"funder_award_id":"No.61872166, No.61662066","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3763998880","display_name":null,"funder_award_id":"61662066","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6224804700","display_name":null,"funder_award_id":"2019YFA0706401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G960422111","display_name":null,"funder_award_id":"61872166","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320313889","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4221131015.pdf","grobid_xml":"https://content.openalex.org/works/W4221131015.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W944118684","https://openalex.org/W1797603343","https://openalex.org/W2003586074","https://openalex.org/W2003657240","https://openalex.org/W2008620264","https://openalex.org/W2018934112","https://openalex.org/W2019619405","https://openalex.org/W2021413283","https://openalex.org/W2022349126","https://openalex.org/W2057857857","https://openalex.org/W2058357179","https://openalex.org/W2058819446","https://openalex.org/W2082374086","https://openalex.org/W2112090702","https://openalex.org/W2337084907","https://openalex.org/W2894987154","https://openalex.org/W2902783036","https://openalex.org/W2906886296","https://openalex.org/W2958947625","https://openalex.org/W3021374038","https://openalex.org/W3032916206","https://openalex.org/W3046345131","https://openalex.org/W3092385961","https://openalex.org/W3098473534","https://openalex.org/W3104262429","https://openalex.org/W3105561612","https://openalex.org/W3119177171","https://openalex.org/W3135574635","https://openalex.org/W3160802980","https://openalex.org/W6655197476","https://openalex.org/W6847388455"],"related_works":["https://openalex.org/W2063086397","https://openalex.org/W2114920609","https://openalex.org/W2129837124","https://openalex.org/W1580095423","https://openalex.org/W2077715071","https://openalex.org/W2484618777","https://openalex.org/W2931395331","https://openalex.org/W2949141875","https://openalex.org/W3135574635","https://openalex.org/W4200232507"],"abstract_inverted_index":{"Characterizing":[0],"the":[1,13,16,25,32,35,51,56,64,74,104,110,121,130,135],"topology":[2],"and":[3,47,81,91,118,124,129],"random":[4,8],"walk":[5],"of":[6,24,58,67,113,132],"a":[7,22,40,100],"network":[9,17,29,38],"is":[10],"difficult":[11],"because":[12],"connections":[14],"in":[15,34,109,134],"are":[18],"uncertain.":[19],"We":[20],"propose":[21],"class":[23],"generalized":[26,68,114],"weighted":[27,69,93,115],"Koch":[28,37,70,116],"by":[30,72],"replacing":[31],"triangles":[33],"traditional":[36],"with":[39],"graph":[41],"Rs":[42],"according":[43],"to":[44,50],"probability":[45],"0\u2264p\u22641":[46],"assign":[48],"weight":[49],"network.":[52,136],"Then,":[53],"we":[54,98],"determine":[55],"range":[57],"several":[59],"indicators":[60],"that":[61],"can":[62],"characterize":[63],"topological":[65],"properties":[66],"networks":[71,117],"examining":[73],"two":[75],"models":[76],"under":[77],"extreme":[78],"conditions,":[79],"p=0":[80],"p=1,":[82],"including":[83],"average":[84,92,105],"degree,":[85],"degree":[86],"distribution,":[87],"clustering":[88],"coefficient,":[89],"diameter,":[90],"shortest":[94],"path.":[95],"In":[96],"addition,":[97],"give":[99],"lower":[101],"bound":[102],"on":[103],"trapping":[106,111],"time":[107],"(ATT)":[108],"problem":[112],"also":[119],"reveal":[120],"linear,":[122],"super-linear,":[123],"sub-linear":[125],"relationships":[126],"between":[127],"ATT":[128],"number":[131],"nodes":[133]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
