{"id":"https://openalex.org/W2012405765","doi":"https://doi.org/10.1145/1190095.1190160","title":"Thresholds for virus spread on networks","display_name":"Thresholds for virus spread on networks","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2012405765","doi":"https://doi.org/10.1145/1190095.1190160","mag":"2012405765"},"language":"en","primary_location":{"id":"doi:10.1145/1190095.1190160","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1190095.1190160","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 1st international conference on Performance evaluation methodolgies and tools - valuetools '06","raw_type":"proceedings-article"},"type":"conference-abstract","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/A5083971005","display_name":"Moez Draief","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Moez Draief","raw_affiliation_strings":["Centre for Mathematical Sciences, Cambridge, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Mathematical Sciences, Cambridge, United Kingdom","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028740271","display_name":"Ayalvadi Ganesh","orcid":"https://orcid.org/0000-0003-3000-0434"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Ayalvadi Ganesh","raw_affiliation_strings":["Microsoft Research, Cambridge, United Kingdom","Microsoft Research, Cambridge, United Kingdom ("],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research, Cambridge, United Kingdom","institution_ids":["https://openalex.org/I4210164937"]},{"raw_affiliation_string":"Microsoft Research, Cambridge, United Kingdom (","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007698196","display_name":"Laurent Massouli\u00e9","orcid":"https://orcid.org/0000-0001-7263-0069"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Laurent Massouli\u00e9","raw_affiliation_strings":["Microsoft Research, Cambridge, United Kingdom","Microsoft Research, Cambridge, United Kingdom ("],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research, Cambridge, United Kingdom","institution_ids":["https://openalex.org/I4210164937"]},{"raw_affiliation_string":"Microsoft Research, Cambridge, United Kingdom (","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"51","last_page":"51"},"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/T10400","display_name":"Network Security and Intrusion Detection","score":0.993399977684021,"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":0.9901000261306763,"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/spectral-radius","display_name":"Spectral radius","score":0.8110030293464661},{"id":"https://openalex.org/keywords/malware","display_name":"Malware","score":0.7519122362136841},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6983442902565002},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.6205297708511353},{"id":"https://openalex.org/keywords/computer-virus","display_name":"Computer virus","score":0.5752946734428406},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5678322315216064},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5390315651893616},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5368466973304749},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4736286997795105},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3888287842273712},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36011868715286255},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.2528361678123474},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18102401494979858},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17785269021987915},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.16539305448532104},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.1261531114578247}],"concepts":[{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.8110030293464661},{"id":"https://openalex.org/C541664917","wikidata":"https://www.wikidata.org/wiki/Q14001","display_name":"Malware","level":2,"score":0.7519122362136841},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6983442902565002},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.6205297708511353},{"id":"https://openalex.org/C19407854","wikidata":"https://www.wikidata.org/wiki/Q485","display_name":"Computer virus","level":2,"score":0.5752946734428406},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5678322315216064},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5390315651893616},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5368466973304749},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4736286997795105},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3888287842273712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36011868715286255},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.2528361678123474},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18102401494979858},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17785269021987915},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.16539305448532104},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.1261531114578247},{"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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1190095.1190160","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1190095.1190160","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 1st international conference on Performance evaluation methodolgies and tools - valuetools '06","raw_type":"proceedings-article"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/58261542-1011-4c92-a062-c73d91b089ca","is_oa":false,"landing_page_url":"https://hdl.handle.net/1983/58261542-1011-4c92-a062-c73d91b089ca","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1914027636","https://openalex.org/W1976969221","https://openalex.org/W2006423444","https://openalex.org/W2008620264","https://openalex.org/W2023955403","https://openalex.org/W2027377866","https://openalex.org/W2036758357","https://openalex.org/W2038195874","https://openalex.org/W2044881936","https://openalex.org/W2049322835","https://openalex.org/W2061118827","https://openalex.org/W2065543353","https://openalex.org/W2068871408","https://openalex.org/W2077697549","https://openalex.org/W2128181433","https://openalex.org/W2129918926","https://openalex.org/W2138359578","https://openalex.org/W2148301044","https://openalex.org/W2152361742","https://openalex.org/W2159919478","https://openalex.org/W2165100126","https://openalex.org/W2324331736","https://openalex.org/W2905110430","https://openalex.org/W2952870388","https://openalex.org/W3144881883"],"related_works":["https://openalex.org/W2097492617","https://openalex.org/W2753240997","https://openalex.org/W1764168690","https://openalex.org/W2107559391","https://openalex.org/W2278418704","https://openalex.org/W2350512268","https://openalex.org/W3170525725","https://openalex.org/W4360996742","https://openalex.org/W2150675148","https://openalex.org/W4376852260"],"abstract_inverted_index":{"We":[0,26,54],"study":[1],"how":[2,56],"the":[3,16,20,57,60,68,76,86,90,93,100,122,141,153,165],"spread":[4,160],"of":[5,19,38,59,78,89,132],"computer":[6],"viruses,":[7],"worms,":[8],"and":[9,48,92],"other":[10],"self-replicating":[11],"malware":[12],"is":[13,83,97,104,119,145],"affected":[14],"by":[15],"logical":[17],"topology":[18],"network":[21,69],"over":[22],"which":[23,31],"they":[24],"propagate.":[25],"consider":[27],"a":[28,108],"model":[29],"in":[30,36,107,128,157,161],"each":[32],"host":[33],"can":[34,111],"be":[35,112],"one":[37],"3":[39],"possible":[40],"states":[41],"-":[42],"susceptible,":[43],"infected":[44,65,95,102,143],"or":[45],"removed":[46],"(cured,":[47],"no":[49],"longer":[50],"susceptible":[51],"to":[52,80],"infection).":[53],"characterise":[55],"size":[58],"population":[61,96,103,144],"that":[62,74,110,140],"eventually":[63],"becomes":[64],"depends":[66],"on":[67],"topology.":[70],"Specifically,":[71],"we":[72,126],"show":[73,127],"if":[75,116],"ratio":[77,118],"cure":[79],"infection":[81],"rates":[82],"larger":[84],"than":[85,121],"spectral":[87,123],"radius":[88],"graph,":[91],"initial":[94],"small,":[98],"then":[99,125],"final":[101,142],"also":[105],"small":[106],"sense":[109],"made":[113],"precise.":[114],"Conversely,":[115],"this":[117],"smaller":[120],"radius,":[124],"some":[129],"graph":[130],"models":[131],"practical":[133],"interest":[134],"(including":[135],"power":[136],"law":[137],"random":[138],"graphs)":[139],"large.":[146],"These":[147],"results":[148],"yield":[149],"insights":[150],"into":[151],"what":[152],"critical":[154],"parameters":[155],"are":[156],"determining":[158],"virus":[159],"networks.A":[162],"category":[163],"with":[164],"(minimum)":[166],"three":[167],"required":[168],"fields":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}
