{"id":"https://openalex.org/W2066519773","doi":"https://doi.org/10.1155/2013/902519","title":"Exact Solutions of a Generalized Weighted Scale Free Network","display_name":"Exact Solutions of a Generalized Weighted Scale Free Network","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2066519773","doi":"https://doi.org/10.1155/2013/902519","mag":"2066519773"},"language":"en","primary_location":{"id":"doi:10.1155/2013/902519","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/902519","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/902519.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/902519.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047902002","display_name":"Li Tan","orcid":"https://orcid.org/0000-0002-1868-7707"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Tan","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China","School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019523347","display_name":"Dingyou Lei","orcid":null},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dingyou Lei","raw_affiliation_strings":["School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019523347"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.09701671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9969000220298767,"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":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7985237836837769},{"id":"https://openalex.org/keywords/scale-free-network","display_name":"Scale-free network","score":0.6378529071807861},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5400195717811584},{"id":"https://openalex.org/keywords/vertex-model","display_name":"Vertex model","score":0.5223113894462585},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4303605556488037},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4263850450515747},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.4232974052429199},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40488195419311523},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.37458962202072144},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32046234607696533},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22195613384246826},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.20692580938339233},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1907196342945099},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16212984919548035}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7985237836837769},{"id":"https://openalex.org/C25580894","wikidata":"https://www.wikidata.org/wiki/Q1071058","display_name":"Scale-free network","level":3,"score":0.6378529071807861},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5400195717811584},{"id":"https://openalex.org/C80183032","wikidata":"https://www.wikidata.org/wiki/Q7922777","display_name":"Vertex model","level":2,"score":0.5223113894462585},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4303605556488037},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4263850450515747},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.4232974052429199},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40488195419311523},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.37458962202072144},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32046234607696533},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22195613384246826},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.20692580938339233},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1907196342945099},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16212984919548035},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/902519","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/902519","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/902519.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1399493308","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1399493308","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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:RePEc:hin:jnljam:902519","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/902519.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:49ec26b6998443d293b96ba945d6c9a8","is_oa":true,"landing_page_url":"https://doaj.org/article/49ec26b6998443d293b96ba945d6c9a8","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":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/902519","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/902519","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/902519.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7900000214576721,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G8068917443","display_name":"\u94c1\u8def\u8d85\u9650\u8d85\u91cd\u8d27\u7269\u8fd0\u8f93\u7ec4\u7ec7\u7406\u8bba\u7814\u7a76","funder_award_id":"70971140","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/F4320321514","display_name":"Central South University","ror":"https://ror.org/00f1zfq44"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2066519773.pdf","grobid_xml":"https://content.openalex.org/works/W2066519773.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1953975752","https://openalex.org/W2008620264","https://openalex.org/W2017546343","https://openalex.org/W2032516423","https://openalex.org/W2044977617","https://openalex.org/W2056380633","https://openalex.org/W2089862187","https://openalex.org/W2112090702","https://openalex.org/W2121821841","https://openalex.org/W2167750933","https://openalex.org/W2769133055"],"related_works":["https://openalex.org/W2017964239","https://openalex.org/W2922108232","https://openalex.org/W2086855886","https://openalex.org/W2050365231","https://openalex.org/W2281204610","https://openalex.org/W2065366397","https://openalex.org/W2279390683","https://openalex.org/W2949141875","https://openalex.org/W2123861509","https://openalex.org/W2066519773"],"abstract_inverted_index":{"We":[0],"investigate":[1],"a":[2],"class":[3],"of":[4,17,24,32],"generalized":[5],"weighted":[6],"scale-free":[7],"networks,":[8],"where":[9],"the":[10,30,41,46,50,55,72],"new":[11],"vertex":[12,47,51,73,75],"connects":[13],"to":[14],"m":[15],"pairs":[16],"vertices":[18],"selected":[19],"preferentially.":[20],"The":[21],"key":[22],"contribution":[23],"this":[25,63],"paper":[26],"is":[27],"that,":[28],"from":[29],"standpoint":[31],"random":[33],"processes,":[34],"we":[35],"provide":[36],"rigorous":[37],"analytic":[38],"solutions":[39],"for":[40,71],"steady":[42],"state":[43],"distributions,":[44],"including":[45],"degree":[48],"distribution,":[49],"strength":[52],"distribution":[53],"and":[54,77],"edge":[56,78],"weight":[57],"distribution.":[58],"Numerical":[59],"simulations":[60],"indicate":[61],"that":[62],"network":[64],"model":[65],"yields":[66],"three":[67],"power":[68],"law":[69],"distributions":[70],"degrees,":[74],"strengths":[76],"weights,":[79],"respectively.":[80]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}