{"id":"https://openalex.org/W4391248807","doi":"https://doi.org/10.1109/tnse.2024.3358369","title":"Mean First-Passage Time and Robustness of Complex Cellular Mobile Communication Network","display_name":"Mean First-Passage Time and Robustness of Complex Cellular Mobile Communication Network","publication_year":2024,"publication_date":"2024-01-26","ids":{"openalex":"https://openalex.org/W4391248807","doi":"https://doi.org/10.1109/tnse.2024.3358369"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2024.3358369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2024.3358369","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076981458","display_name":"Jia\u2010Bao Liu","orcid":"https://orcid.org/0000-0002-9620-7692"},"institutions":[{"id":"https://openalex.org/I118987531","display_name":"Anhui Jianzhu University","ror":"https://ror.org/0108wjw08","country_code":"CN","type":"education","lineage":["https://openalex.org/I118987531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia-Bao Liu","raw_affiliation_strings":["School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-9620-7692","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China","institution_ids":["https://openalex.org/I118987531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021103157","display_name":"Xue Zhang","orcid":"https://orcid.org/0009-0006-3876-4243"},"institutions":[{"id":"https://openalex.org/I118987531","display_name":"Anhui Jianzhu University","ror":"https://ror.org/0108wjw08","country_code":"CN","type":"education","lineage":["https://openalex.org/I118987531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xue Zhang","raw_affiliation_strings":["School of Electronics and Information Engineering, Anhui Jianzhu University, Hefei, China"],"raw_orcid":"https://orcid.org/0009-0006-3876-4243","affiliations":[{"raw_affiliation_string":"School of Electronics and Information Engineering, Anhui Jianzhu University, Hefei, China","institution_ids":["https://openalex.org/I118987531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017808266","display_name":"Jinde Cao","orcid":"https://orcid.org/0000-0003-3133-7119"},"institutions":[{"id":"https://openalex.org/I4210155350","display_name":"Purple Mountain Laboratories","ror":"https://ror.org/04zcbk583","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210155350"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinde Cao","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China","Purple Mountain Laboratories, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-3133-7119","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"Purple Mountain Laboratories, Nanjing, China","institution_ids":["https://openalex.org/I4210155350"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100430192","display_name":"Liping Chen","orcid":"https://orcid.org/0000-0002-8110-5378"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liping Chen","raw_affiliation_strings":["School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-8110-5378","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China","institution_ids":["https://openalex.org/I16365422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.8461,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.99425855,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"11","issue":"3","first_page":"3066","last_page":"3076"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11896","display_name":"Opportunistic and Delay-Tolerant Networks","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.7695553302764893},{"id":"https://openalex.org/keywords/mathematical-notation","display_name":"Mathematical notation","score":0.46912598609924316},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.45906972885131836},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4554152488708496},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39833536744117737},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38156408071517944},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3734782934188843},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34272491931915283},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.14725971221923828},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.06832218170166016}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7695553302764893},{"id":"https://openalex.org/C24457124","wikidata":"https://www.wikidata.org/wiki/Q1140046","display_name":"Mathematical notation","level":3,"score":0.46912598609924316},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.45906972885131836},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4554152488708496},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39833536744117737},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38156408071517944},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3734782934188843},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34272491931915283},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.14725971221923828},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.06832218170166016}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tnse.2024.3358369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2024.3358369","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4090591332","display_name":null,"funder_award_id":"2008085J01","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"},{"id":"https://openalex.org/G8022360373","display_name":null,"funder_award_id":"62073114","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/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W1964062850","https://openalex.org/W1995519784","https://openalex.org/W1997887535","https://openalex.org/W2003586074","https://openalex.org/W2008209917","https://openalex.org/W2015117969","https://openalex.org/W2022363230","https://openalex.org/W2024217986","https://openalex.org/W2043852692","https://openalex.org/W2051046255","https://openalex.org/W2056711961","https://openalex.org/W2073676069","https://openalex.org/W2075878420","https://openalex.org/W2082503049","https://openalex.org/W2149141576","https://openalex.org/W2164727176","https://openalex.org/W2236900448","https://openalex.org/W2505741526","https://openalex.org/W2513327292","https://openalex.org/W2523664694","https://openalex.org/W2548101300","https://openalex.org/W2566971417","https://openalex.org/W2746696930","https://openalex.org/W2765560143","https://openalex.org/W2794020843","https://openalex.org/W2794067940","https://openalex.org/W2884093134","https://openalex.org/W2892404678","https://openalex.org/W2901536684","https://openalex.org/W2924340414","https://openalex.org/W2938681029","https://openalex.org/W2948136331","https://openalex.org/W2954184251","https://openalex.org/W2963302977","https://openalex.org/W2963330659","https://openalex.org/W2981207193","https://openalex.org/W2995403194","https://openalex.org/W2996631030","https://openalex.org/W3000421666","https://openalex.org/W3042714488","https://openalex.org/W3090584132","https://openalex.org/W3098657114","https://openalex.org/W3101342997","https://openalex.org/W3101662986","https://openalex.org/W3104213302","https://openalex.org/W3105946119","https://openalex.org/W3120670948","https://openalex.org/W3120672808","https://openalex.org/W3150479692","https://openalex.org/W3158807927","https://openalex.org/W3199698207","https://openalex.org/W3215733096","https://openalex.org/W4206554609","https://openalex.org/W4282982693","https://openalex.org/W4286579123","https://openalex.org/W4294691738","https://openalex.org/W4309913260","https://openalex.org/W6788632106"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1968256718","https://openalex.org/W2393607213","https://openalex.org/W2495832077","https://openalex.org/W2278797713","https://openalex.org/W98357545","https://openalex.org/W977407476","https://openalex.org/W4249487612","https://openalex.org/W2624682093","https://openalex.org/W4280602899"],"abstract_inverted_index":{"With":[0],"the":[1,9,31,46,55,59,68,72,112,129,132,139,147,153,162,165,168,171,177,185,194,198,214],"rapid":[2],"development":[3],"of":[4,11,48,58,67,84,115,131,164,170,188,197,200,210,216],"complex":[5,49],"network":[6,35,40,50,106,155,172,204,218],"science":[7],"and":[8,71,96,109,179],"complexity":[10],"communication":[12,34,217],"network,":[13,167],"it":[14,135],"is":[15,121,136,156,173,190,209],"difficult":[16],"to":[17,24,88,91,128,159,192,213],"research":[18,215],"its":[19],"technical":[20],"application.":[21],"In":[22],"order":[23],"solve":[25],"these":[26],"problems,":[27],"we":[28,53],"firstly":[29],"design":[30],"cellular":[32],"mobile":[33],"as":[36],"a":[37],"fractal":[38],"six-star":[39,166],"<inline-formula":[41,63,76,92,97,117],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[42,64,77,93,98,118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[43,65,78,94,99,119],"notation=\"LaTeX\">$G_{t,s}$</tex-math></inline-formula>":[44],"from":[45],"view":[47],"science.":[51],"Secondly,":[52],"investigate":[54],"analytical":[56],"expression":[57,114],"mean":[60],"first-passage":[61],"time":[62,110],"notation=\"LaTeX\">$M_{G_{t,s}}$</tex-math></inline-formula>":[66],"random":[69],"walk":[70],"average":[73,186],"path":[74],"length":[75],"notation=\"LaTeX\">$\\left\\langle":[79],"W":[80],"\\right\\rangle$</tex-math></inline-formula>":[81],".":[82,101],"Both":[83],"them":[85],"are":[86,142,181],"proved":[87],"be":[89],"proportional":[90],"notation=\"LaTeX\">$t$</tex-math></inline-formula>":[95],"notation=\"LaTeX\">$s$</tex-math></inline-formula>":[100],"Thirdly,":[102],"taking":[103],"into":[104],"account":[105],"transmission":[107],"efficiency":[108],"delay,":[111],"recursive":[113],"diameter":[116],"notation=\"LaTeX\">$D_{t}$</tex-math></inline-formula>":[120],"derived,":[122],"which":[123,150,175,208],"increases":[124],"exponentially":[125],"with":[126,146],"respect":[127],"size":[130],"network.":[133],"Fourthly,":[134],"verified":[137],"that":[138,152],"experimental":[140],"simulations":[141],"in":[143,219],"perfect":[144],"consistent":[145],"theoretical":[148],"analysis,":[149],"shows":[151],"designed":[154],"reasonable.":[157],"Fifthly,":[158],"further":[160],"proving":[161],"stability":[163],"robustness":[169,178],"analyzed,":[174],"indicates":[176],"density":[180],"positively":[182],"correlated.":[183],"Finally,":[184],"value":[187],"experiments":[189],"used":[191],"analyze":[193],"decisive":[195],"effect":[196],"number":[199],"nodes":[201],"removed":[202],"after":[203],"failure":[205],"on":[206],"robustness,":[207],"great":[211],"significance":[212],"reality.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":13},{"year":2025,"cited_by_count":25},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}