{"id":"https://openalex.org/W2998770966","doi":"https://doi.org/10.37236/7832","title":"Bootstrap Percolation in Directed Inhomogeneous Random Graphs","display_name":"Bootstrap Percolation in Directed Inhomogeneous Random Graphs","publication_year":2019,"publication_date":"2019-07-19","ids":{"openalex":"https://openalex.org/W2998770966","doi":"https://doi.org/10.37236/7832","mag":"2998770966"},"language":"en","primary_location":{"id":"doi:10.37236/7832","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7832","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p12/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p12/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065755537","display_name":"Thilo Meyer\u2010Brandis","orcid":"https://orcid.org/0000-0002-6374-7983"},"institutions":[{"id":"https://openalex.org/I4210127848","display_name":"Institut f\u00fcr Urheber- und Medienrecht","ror":"https://ror.org/035pp4s04","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210127848"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thilo Meyer-Brandis","raw_affiliation_strings":["University of Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Munich","institution_ids":["https://openalex.org/I4210127848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008841359","display_name":"Nils Detering","orcid":"https://orcid.org/0000-0002-5251-5407"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nils Detering","raw_affiliation_strings":["University of California, Santa Barbara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075970062","display_name":"\u039a\u03c9\u03bd\u03c3\u03c4\u03b1\u03bd\u03c4\u03af\u03bd\u03bf\u03c2 \u03a0\u03b1\u03bd\u03b1\u03b3\u03b9\u03ce\u03c4\u03bf\u03c5","orcid":"https://orcid.org/0000-0002-9258-6082"},"institutions":[{"id":"https://openalex.org/I4210127848","display_name":"Institut f\u00fcr Urheber- und Medienrecht","ror":"https://ror.org/035pp4s04","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210127848"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Konstantinos Panagiotou","raw_affiliation_strings":["University of Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Munich","institution_ids":["https://openalex.org/I4210127848"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1535,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.79248943,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"3","first_page":null,"last_page":null},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9878000020980835,"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/combinatorics","display_name":"Combinatorics","score":0.6650365591049194},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6469606757164001},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6209518313407898},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.6130856871604919},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5620776414871216},{"id":"https://openalex.org/keywords/percolation-threshold","display_name":"Percolation threshold","score":0.4413217008113861},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42119163274765015},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38130709528923035},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.22806769609451294},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10423806309700012}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6650365591049194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6469606757164001},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6209518313407898},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.6130856871604919},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5620776414871216},{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.4413217008113861},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42119163274765015},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38130709528923035},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.22806769609451294},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10423806309700012},{"id":"https://openalex.org/C69990965","wikidata":"https://www.wikidata.org/wiki/Q65402698","display_name":"Electrical resistivity and conductivity","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/7832","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7832","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p12/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/7832","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7832","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p12/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2998770966.pdf","grobid_xml":"https://content.openalex.org/works/W2998770966.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W160842944","https://openalex.org/W403359422","https://openalex.org/W600933876","https://openalex.org/W1495430942","https://openalex.org/W1584575186","https://openalex.org/W1979720612","https://openalex.org/W1987070596","https://openalex.org/W1990831624","https://openalex.org/W2027223596","https://openalex.org/W2027508917","https://openalex.org/W2035529977","https://openalex.org/W2057505998","https://openalex.org/W2092170472","https://openalex.org/W2093333397","https://openalex.org/W2112976607","https://openalex.org/W2114138382","https://openalex.org/W2116818317","https://openalex.org/W2125271247","https://openalex.org/W2145895674","https://openalex.org/W2148896022","https://openalex.org/W2156051808","https://openalex.org/W2157925905","https://openalex.org/W2276192920","https://openalex.org/W2610631722","https://openalex.org/W2769133055","https://openalex.org/W2950850272","https://openalex.org/W2964152523","https://openalex.org/W2964202470","https://openalex.org/W3125263907","https://openalex.org/W3126101873","https://openalex.org/W4252001504","https://openalex.org/W4292027056","https://openalex.org/W4385634913","https://openalex.org/W4392733169","https://openalex.org/W6657313492","https://openalex.org/W6682670483","https://openalex.org/W6683089644","https://openalex.org/W6695126602"],"related_works":["https://openalex.org/W1719252778","https://openalex.org/W922283457","https://openalex.org/W2031098440","https://openalex.org/W4307385446","https://openalex.org/W2466894780","https://openalex.org/W3092119098","https://openalex.org/W2003008160","https://openalex.org/W2381713449","https://openalex.org/W2731724293","https://openalex.org/W2904724461"],"abstract_inverted_index":{"Bootstrap":[0],"percolation":[1,60],"is":[2,6,26,77,115],"a":[3,16,55,62,131,150,180],"process":[4],"that":[5,41,107,161,186],"used":[7],"to":[8,84,92,97,100,129,165,173,190],"describe":[9],"the":[10,20,35,43,72,75,88,104,108,113,119,137,142,156,177],"spread":[11],"of":[12,37,58,65,74,90,112,122,133,158,176],"an":[13,29,146],"infection":[14],"on":[15,61],"given":[17],"graph.":[18],"In":[19],"model":[21,64,126],"considered":[22],"here":[23],"each":[24,85],"vertex":[25,44],"equipped":[27],"with":[28],"individual":[30],"threshold.":[31],"As":[32,149],"soon":[33],"as":[34,47],"number":[36],"infected":[38,46,123],"neighbors":[39],"exceeds":[40],"threshold,":[42],"gets":[45],"well":[48],"and":[49,67,182],"remains":[50],"so":[51],"forever.":[52],"We":[53],"perform":[54],"thorough":[56],"analysis":[57],"bootstrap":[59],"novel":[63,184],"directed":[66],"inhomogeneous":[68],"random":[69],"graphs,":[70],"where":[71],"distribution":[73,111,144],"edges":[76,94,99],"specied":[78],"by":[79],"assigning":[80],"two":[81],"distinct":[82],"weights":[83],"vertex,":[86],"describing":[87],"tendency":[89],"it":[91],"receive":[93],"from":[95],"or":[96],"send":[98],"other":[101],"vertices.":[102,124],"Under":[103],"mild":[105],"assumption":[106],"limiting":[109],"degree":[110,143],"graph":[114,178],"integrable":[116],"we":[117,154,163],"determine":[118],"typical":[120],"fraction":[121],"Our":[125],"allows":[127],"us":[128],"study":[130],"variety":[132],"settings,":[134],"in":[135,140],"particular":[136],"prominent":[138],"case":[139],"which":[141],"has":[145],"unbounded":[147],"variance.":[148],"second":[151],"main":[152],"contribution,":[153],"quantify":[155],"notion":[157],"\"systemic":[159],"risk\",":[160],"is,":[162],"characterize":[164],"what":[166],"extent":[167],"tiny":[168],"initial":[169],"infections":[170],"can":[171],"propagate":[172],"large":[174],"parts":[175],"through":[179],"cascade,":[181],"discover":[183],"features":[185],"make":[187],"graphs":[188],"prone/resilient":[189],"initially":[191],"small":[192],"infections.":[193]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
