{"id":"https://openalex.org/W2274264080","doi":"https://doi.org/10.1093/comnet/cnv021","title":"Complex contagions and hybrid phase transitions","display_name":"Complex contagions and hybrid phase transitions","publication_year":2015,"publication_date":"2015-08-14","ids":{"openalex":"https://openalex.org/W2274264080","doi":"https://doi.org/10.1093/comnet/cnv021","mag":"2274264080"},"language":"en","primary_location":{"id":"doi:10.1093/comnet/cnv021","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnv021","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"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":"Journal of Complex Networks","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/A5102959104","display_name":"Joel C. Miller","orcid":"https://orcid.org/0000-0003-4426-0405"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Joel C. Miller","raw_affiliation_strings":["School of Mathematical Sciences and School of Biological Sciences, Monash University, Clayton, VIC Australia, Monash Academy for Cross and Interdisciplinary Mathematics"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and School of Biological Sciences, Monash University, Clayton, VIC Australia, Monash Academy for Cross and Interdisciplinary Mathematics","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102959104"],"corresponding_institution_ids":["https://openalex.org/I56590836"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":3.318,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.92243004,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"4","issue":"2","first_page":"201","last_page":"223"},"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9970999956130981,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6122670769691467},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5939628481864929},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.5046261548995972},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4895723760128021},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.4871103763580322},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.48298823833465576},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48293349146842957},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4780876338481903},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.446536660194397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2715739607810974},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24030715227127075},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2042762041091919},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18269082903862}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6122670769691467},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5939628481864929},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.5046261548995972},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4895723760128021},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.4871103763580322},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.48298823833465576},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48293349146842957},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4780876338481903},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.446536660194397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2715739607810974},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24030715227127075},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2042762041091919},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18269082903862},{"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/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/comnet/cnv021","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comnet/cnv021","pdf_url":null,"source":{"id":"https://openalex.org/S2531583244","display_name":"Journal of Complex Networks","issn_l":"2051-1310","issn":["2051-1310","2051-1329"],"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":"Journal of Complex Networks","raw_type":"journal-article"},{"id":"pmh:oai:open-archive.highwire.org:comnet:4/2/201","is_oa":false,"landing_page_url":"http://comnet.oxfordjournals.org/cgi/content/short/4/2/201","pdf_url":null,"source":{"id":"https://openalex.org/S4406923041","display_name":"HighWire Press Open Archive","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"TEXT"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1504429442","https://openalex.org/W1584575186","https://openalex.org/W1628014767","https://openalex.org/W1889439171","https://openalex.org/W1963983289","https://openalex.org/W1965092067","https://openalex.org/W1967608252","https://openalex.org/W1970903602","https://openalex.org/W1973374221","https://openalex.org/W1977872462","https://openalex.org/W1982591743","https://openalex.org/W1987499067","https://openalex.org/W1992015378","https://openalex.org/W1994731130","https://openalex.org/W1998023974","https://openalex.org/W1998717040","https://openalex.org/W2000687288","https://openalex.org/W2000964073","https://openalex.org/W2008277821","https://openalex.org/W2008453806","https://openalex.org/W2016468753","https://openalex.org/W2027508917","https://openalex.org/W2028985170","https://openalex.org/W2029197563","https://openalex.org/W2033958672","https://openalex.org/W2053511879","https://openalex.org/W2064168048","https://openalex.org/W2070963710","https://openalex.org/W2089899018","https://openalex.org/W2114696370","https://openalex.org/W2115040920","https://openalex.org/W2130863673","https://openalex.org/W2138582543","https://openalex.org/W2140984072","https://openalex.org/W2141206236","https://openalex.org/W2150208547","https://openalex.org/W2151223815","https://openalex.org/W2153349054","https://openalex.org/W2158616180","https://openalex.org/W2164928285","https://openalex.org/W2952633294","https://openalex.org/W2963370796","https://openalex.org/W3102629383","https://openalex.org/W3103776742","https://openalex.org/W3104100506"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W4300101996","https://openalex.org/W2165950148","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W4403053866","https://openalex.org/W2999294032","https://openalex.org/W3016844740"],"abstract_inverted_index":{"A":[0],"complex":[1,76],"contagion":[2],"is":[3,155],"an":[4,24,130,185],"infectious":[5,125],"process":[6],"in":[7,63,96,104,113,140,235,257,273,280],"which":[8,181],"individuals":[9,41,108,246],"may":[10,38],"require":[11],"multiple":[12],"transmissions":[13],"before":[14],"changing":[15],"state.":[16],"These":[17,59],"are":[18,50,78,207],"used":[19],"to":[20,110,128,163,230,286],"model":[21,90,142,154,275],"behaviours":[22],"if":[23,238],"individual":[25],"only":[26],"adopts":[27],"a":[28,33,53,64,100,145,192],"particular":[29],"behaviour":[30],"after":[31],"perceiving":[32],"consensus":[34],"among":[35],"others.":[36],"We":[37,120,160,199,221,232],"think":[39],"of":[40,56,66,75,86,137,147,169,194,268],"as":[42,99],"beginning":[43],"inactive":[44],"and":[45,144,158,263,292],"becoming":[46],"active":[47,57],"once":[48],"they":[49],"contacted":[51],"by":[52],"sufficient":[54,223],"number":[55,65],"partners.":[58],"have":[60],"been":[61],"studied":[62],"cases,":[67,237],"but":[68,214],"analytic":[69,132],"models":[70,133],"for":[71,124,134,196,210,216,225],"the":[72,84,87,114,135,138,167,170,173,239,253,261,266],"dynamic":[73],"spread":[74,262],"contagions":[77],"typically":[79],"complex.":[80],"Here":[81],"we":[82,177,251],"study":[83],"dynamics":[85,136,168],"Watts":[88,195,269],"threshold":[89],"(WTM)":[91],"assuming":[92],"that":[93,234,265,270],"transmission":[94],"occurs":[95],"continuous":[97],"time":[98,106,115],"Poisson":[101],"process,":[102],"or":[103,259],"discrete":[105],"where":[107],"transmit":[109],"all":[111,245],"partners":[112],"step":[116],"following":[117],"their":[118],"infection.":[119],"adapt":[121],"techniques":[122],"developed":[123],"disease":[126],"modelling":[127],"develop":[129],"analyse":[131],"WTM":[139],"configuration":[141,274],"networks":[143,276],"class":[146],"random":[148],"clustered":[149],"(triangle-based)":[150],"networks.":[151],"The":[152],"resulting":[153],"relatively":[156],"simple":[157],"compact.":[159],"use":[161],"it":[162],"gain":[164],"insights":[165],"into":[166],"contagion.":[171],"Taking":[172],"infinite":[174],"population":[175],"limit,":[176],"derive":[178,222,293],"conditions":[179,224],"under":[180],"cascades":[182,206],"happen":[183],"with":[184],"arbitrarily":[186],"small":[187,211],"initial":[188,212,219],"proportion":[189],"active,":[190],"confirming":[191],"hypothesis":[193,267],"this":[197,226],"case.":[198],"also":[200],"observe":[201],"hybrid":[202,227,240],"phase":[203,228,241],"transitions":[204],"when":[205],"not":[208,278],"possible":[209],"conditions,":[213],"occur":[215],"large":[217],"enough":[218],"conditions.":[220],"transition":[229,242],"occur.":[231],"show":[233],"many":[236,288],"occurs,":[243],"then":[244],"eventually":[247],"become":[248],"active.":[249],"Finally,":[250],"discuss":[252],"role":[254],"clustering":[255],"plays":[256],"facilitating":[258],"impeding":[260],"find":[264],"was":[271],"confirmed":[272],"does":[277],"hold":[279],"general.":[281],"This":[282],"approach":[283],"allows":[284],"us":[285],"unify":[287],"existing":[289],"disparate":[290],"observations":[291],"new":[294],"results.":[295]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}