{"id":"https://openalex.org/W1501825524","doi":"https://doi.org/10.1109/reldis.2003.1238052","title":"Epidemic spreading in real networks: an eigenvalue viewpoint","display_name":"Epidemic spreading in real networks: an eigenvalue viewpoint","publication_year":2004,"publication_date":"2004-03-02","ids":{"openalex":"https://openalex.org/W1501825524","doi":"https://doi.org/10.1109/reldis.2003.1238052","mag":"1501825524"},"language":"en","primary_location":{"id":"doi:10.1109/reldis.2003.1238052","is_oa":false,"landing_page_url":"https://doi.org/10.1109/reldis.2003.1238052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings.","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Epidemic_Spreading_in_Real_Networks_An_Eigenvalue_Viewpoint/6605204","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101657244","display_name":"Yang Wang","orcid":"https://orcid.org/0000-0002-8333-0843"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yang Wang","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078048346","display_name":"Deepayan Chakrabarti","orcid":"https://orcid.org/0000-0002-3863-4928"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Chakrabarti","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100334379","display_name":"Chenxi Wang","orcid":"https://orcid.org/0000-0003-2967-3260"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chenxi Wang","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035605036","display_name":"Christos Faloutsos","orcid":"https://orcid.org/0000-0003-2996-9790"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Faloutsos","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101657244"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":16.0014,"has_fulltext":false,"cited_by_count":863,"citation_normalized_percentile":{"value":0.99554235,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"25","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":1.0,"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":1.0,"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/T11476","display_name":"Graph theory and applications","score":0.9907000064849854,"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/adjacency-matrix","display_name":"Adjacency matrix","score":0.8209806680679321},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7063134908676147},{"id":"https://openalex.org/keywords/threshold-model","display_name":"Threshold model","score":0.607720673084259},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46841374039649963},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4467528164386749},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43467456102371216},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.425773561000824},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4238923192024231},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39324188232421875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37025320529937744},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3499637246131897},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3158456087112427},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1014845073223114},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09065288305282593}],"concepts":[{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.8209806680679321},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7063134908676147},{"id":"https://openalex.org/C202632270","wikidata":"https://www.wikidata.org/wiki/Q7798106","display_name":"Threshold model","level":2,"score":0.607720673084259},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46841374039649963},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4467528164386749},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43467456102371216},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.425773561000824},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4238923192024231},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39324188232421875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37025320529937744},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3499637246131897},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3158456087112427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1014845073223114},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09065288305282593},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1109/reldis.2003.1238052","is_oa":false,"landing_page_url":"https://doi.org/10.1109/reldis.2003.1238052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings.","raw_type":"proceedings-article"},{"id":"pmh:oai:repository.cmu.edu:compsci-1543","is_oa":false,"landing_page_url":"http://repository.cmu.edu/cgi/viewcontent.cgi?article=1543&context=compsci","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Science Department","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6605204","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":null,"raw_type":"Journal contribution"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.129.2340","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.2340","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~deepay/mywww/papers/srds03.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.69.8021","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.8021","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.db.cs.cmu.edu/db-site/Pubs/Lib/srds2003spreadingNetwork/deepay_spreadingNetwork.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.5292","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.5292","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-2.cs.cmu.edu/afs/cs.cmu.edu/user/christos/www/PUBLICATIONS/srds03-virus.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.88.9226","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.9226","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~deepay/mywww/papers/srds03.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/6605204","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Epidemic_Spreading_in_Real_Networks_An_Eigenvalue_Viewpoint/6605204","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.1184/r1/6605204.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6605204.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/6605204","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Epidemic_Spreading_in_Real_Networks_An_Eigenvalue_Viewpoint/6605204","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being","score":0.8700000047683716}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W114870970","https://openalex.org/W1494160116","https://openalex.org/W1498585374","https://openalex.org/W1589703745","https://openalex.org/W1654211971","https://openalex.org/W1976969221","https://openalex.org/W1981589225","https://openalex.org/W2008620264","https://openalex.org/W2038063928","https://openalex.org/W2038195874","https://openalex.org/W2042123098","https://openalex.org/W2042728064","https://openalex.org/W2055620707","https://openalex.org/W2059239694","https://openalex.org/W2108050790","https://openalex.org/W2123279152","https://openalex.org/W2124486211","https://openalex.org/W2136525561","https://openalex.org/W2140697769","https://openalex.org/W2151626491","https://openalex.org/W2166996117","https://openalex.org/W2169082384","https://openalex.org/W2997134027","https://openalex.org/W3103141125","https://openalex.org/W3217684393","https://openalex.org/W4241669766","https://openalex.org/W4252678302","https://openalex.org/W6629466543","https://openalex.org/W6629791766","https://openalex.org/W6635289692","https://openalex.org/W6636851552"],"related_works":["https://openalex.org/W1598955744","https://openalex.org/W2165749285","https://openalex.org/W4285167822","https://openalex.org/W2551731678","https://openalex.org/W2951710344","https://openalex.org/W2204136089","https://openalex.org/W2062626603","https://openalex.org/W2144602163","https://openalex.org/W4384111961","https://openalex.org/W1501825524"],"abstract_inverted_index":{"How":[0,18],"will":[1],"a":[2,6,15,25,61,81],"virus":[3,34,48],"propagate":[4],"in":[5,50],"real":[7,54],"network?":[8],"Does":[9],"an":[10],"epidemic":[11,63,78,109,115],"threshold":[12,64,79,116,134,146],"exist":[13],"for":[14,80,95,122,138,149],"finite":[16],"graph?":[17],"long":[19],"does":[20],"it":[21],"take":[22],"to":[23,68,86,104,136],"disinfect":[24],"network":[26,52,57,82],"given":[27],"particular":[28],"values":[29],"of":[30,90],"infection":[31],"rate":[32],"and":[33,55],"death":[35],"rate?":[36],"We":[37,59,111,142],"answer":[38],"the":[39,77,87,96,108,133],"first":[40],"question":[41],"by":[42],"providing":[43],"equations":[44],"that":[45,66,101,113,132,144],"accurately":[46],"model":[47,117],"propagation":[49],"any":[51],"including":[53],"synthesized":[56],"graphs.":[58,141,151],"propose":[60],"general":[62],"condition":[65,147],"applies":[67],"arbitrary":[69,150],"graphs:":[70],"we":[71,99,130],"prove":[72],"that,":[73],"under":[74],"reasonable":[75],"approximations,":[76],"is":[83],"closely":[84],"related":[85],"largest":[88],"eigenvalue":[89],"its":[91],"adjacency":[92],"matrix.":[93],"Finally,":[94],"last":[97],"question,":[98],"show":[100,112,131,143],"infections":[102],"tend":[103],"zero":[105,137],"exponentially":[106],"below":[107],"threshold.":[110],"our":[114,145],"subsumes":[118],"many":[119],"known":[120],"thresholds":[121],"special-case":[123],"graphs":[124],"(e.g.,":[125],"Erdos-Renyi,":[126],"BA":[127],"power-law,":[128],"homogeneous);":[129],"tends":[135],"infinite":[139],"power-law":[140],"holds":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":55},{"year":2021,"cited_by_count":55},{"year":2020,"cited_by_count":69},{"year":2019,"cited_by_count":39},{"year":2018,"cited_by_count":63},{"year":2017,"cited_by_count":54},{"year":2016,"cited_by_count":66},{"year":2015,"cited_by_count":71},{"year":2014,"cited_by_count":82},{"year":2013,"cited_by_count":49},{"year":2012,"cited_by_count":32}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}