{"id":"https://openalex.org/W2059010219","doi":"https://doi.org/10.1142/s0218127410026216","title":"EVOLUTION OF HETEROGENEOUS NETWORKS UNDER PREFERENTIAL ATTACHMENT","display_name":"EVOLUTION OF HETEROGENEOUS NETWORKS UNDER PREFERENTIAL ATTACHMENT","publication_year":2010,"publication_date":"2010-03-01","ids":{"openalex":"https://openalex.org/W2059010219","doi":"https://doi.org/10.1142/s0218127410026216","mag":"2059010219"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127410026216","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410026216","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5112490129","display_name":"A. Santiago","orcid":null},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"ANTONIO SANTIAGO","raw_affiliation_strings":["Grupo de Sistemas Complejos, Departamento de F\u00edsica ETSIA, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Grupo de Sistemas Complejos, Departamento de F\u00edsica ETSIA, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029099160","display_name":"R. M. Benito","orcid":"https://orcid.org/0000-0003-3949-8232"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"ROSA M. BENITO","raw_affiliation_strings":["Grupo de Sistemas Complejos, Departamento de F\u00edsica ETSIA, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Grupo de Sistemas Complejos, Departamento de F\u00edsica ETSIA, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.14397814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"03","first_page":"923","last_page":"927"},"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9925000071525574,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9721999764442444,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/preferential-attachment","display_name":"Preferential attachment","score":0.90459805727005},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.7354744672775269},{"id":"https://openalex.org/keywords/heterogeneous-network","display_name":"Heterogeneous network","score":0.5972362756729126},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5898669958114624},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5660192370414734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5257202982902527},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5252109169960022},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5241011381149292},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.5057449340820312},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4624832570552826},{"id":"https://openalex.org/keywords/offset","display_name":"Offset (computer science)","score":0.45693886280059814},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.418149471282959},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37469595670700073},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3478632867336273},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2890594005584717},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20392867922782898},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.19934329390525818},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16487973928451538},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1620723307132721},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08865916728973389},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08775195479393005},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.0706774890422821}],"concepts":[{"id":"https://openalex.org/C2780600066","wikidata":"https://www.wikidata.org/wiki/Q7239828","display_name":"Preferential attachment","level":3,"score":0.90459805727005},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.7354744672775269},{"id":"https://openalex.org/C158207573","wikidata":"https://www.wikidata.org/wiki/Q5747224","display_name":"Heterogeneous network","level":4,"score":0.5972362756729126},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5898669958114624},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5660192370414734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5257202982902527},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5252109169960022},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5241011381149292},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.5057449340820312},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4624832570552826},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.45693886280059814},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.418149471282959},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37469595670700073},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3478632867336273},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2890594005584717},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20392867922782898},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.19934329390525818},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16487973928451538},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1620723307132721},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08865916728973389},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08775195479393005},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0706774890422821},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.0},{"id":"https://openalex.org/C108037233","wikidata":"https://www.wikidata.org/wiki/Q11375","display_name":"Wireless network","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127410026216","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410026216","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1953975752","https://openalex.org/W1995373933","https://openalex.org/W2008620264","https://openalex.org/W2032516423","https://openalex.org/W2036671379","https://openalex.org/W2048530992","https://openalex.org/W2055628931","https://openalex.org/W2070722739","https://openalex.org/W2088209891","https://openalex.org/W2121821841","https://openalex.org/W2124637492","https://openalex.org/W2136931666","https://openalex.org/W2148606196","https://openalex.org/W2164727176","https://openalex.org/W2418582869","https://openalex.org/W3101672529"],"related_works":["https://openalex.org/W1560913374","https://openalex.org/W2141185052","https://openalex.org/W230111105","https://openalex.org/W2341322822","https://openalex.org/W2976337371","https://openalex.org/W1981257001","https://openalex.org/W2922108232","https://openalex.org/W3101672529","https://openalex.org/W4288103010","https://openalex.org/W3013262114"],"abstract_inverted_index":{"In":[0,27],"this":[1,28],"paper,":[2],"we":[3],"present":[4],"results":[5],"concerning":[6],"a":[7,18,35,59],"natural":[8],"extension":[9],"of":[10,13,20,52,80],"the":[11,21,31,49,55,78,81,84],"class":[12,57],"heterogeneous":[14,25],"preferential":[15],"attachment":[16,85],"models,":[17],"generalization":[19],"Barab\u00e1si\u2013Albert":[22],"model":[23],"to":[24],"networks.":[26],"extended":[29,56],"class,":[30],"network":[32],"nodes":[33],"enjoy":[34],"nonzero":[36],"attractiveness":[37],"even":[38],"when":[39],"their":[40,64,72],"connectivity":[41],"degrees":[42],"are":[43],"zero.":[44],"We":[45],"analytically":[46],"show":[47],"that":[48,68],"degree":[50,73],"densities":[51],"models":[53],"in":[54,71,77,83],"exhibit":[58],"richer":[60],"scaling":[61,70],"behavior":[62],"than":[63],"homogeneous":[65],"counterparts,":[66],"and":[67],"power-law":[69],"distribution":[74],"is":[75],"robust":[76],"presence":[79],"offset":[82],"kernel.":[86]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}