Identifying influential spreaders by gravity model

Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information, innovations, behaviors, and so on. Inspired by the gravity law, we propose a gravity model that utilizes both neighborhood information and pa...

Full description

Saved in:
Bibliographic Details
Published inScientific reports Vol. 9; no. 1; p. 8387
Main Authors Li, Zhe, Ren, Tao, Ma, Xiaoqi, Liu, Simiao, Zhang, Yixin, Zhou, Tao
Format Journal Article
LanguageEnglish
Published London Nature Publishing Group UK 10.06.2019
Nature Publishing Group
Subjects
Online AccessGet full text

Cover

Loading…
Abstract Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information, innovations, behaviors, and so on. Inspired by the gravity law, we propose a gravity model that utilizes both neighborhood information and path information to measure a node’s importance in spreading dynamics. In order to reduce the accumulated errors caused by interactions at distance and to lower the computational complexity, a local version of the gravity model is further proposed by introducing a truncation radius. Empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on fourteen real networks show that the gravity model and the local gravity model perform very competitively in comparison with well-known state-of-the-art methods. For the local gravity model, the empirical results suggest an approximately linear relation between the optimal truncation radius and the average distance of the network.
AbstractList Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information, innovations, behaviors, and so on. Inspired by the gravity law, we propose a gravity model that utilizes both neighborhood information and path information to measure a node’s importance in spreading dynamics. In order to reduce the accumulated errors caused by interactions at distance and to lower the computational complexity, a local version of the gravity model is further proposed by introducing a truncation radius. Empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on fourteen real networks show that the gravity model and the local gravity model perform very competitively in comparison with well-known state-of-the-art methods. For the local gravity model, the empirical results suggest an approximately linear relation between the optimal truncation radius and the average distance of the network.
Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information, innovations, behaviors, and so on. Inspired by the gravity law, we propose a gravity model that utilizes both neighborhood information and path information to measure a node's importance in spreading dynamics. In order to reduce the accumulated errors caused by interactions at distance and to lower the computational complexity, a local version of the gravity model is further proposed by introducing a truncation radius. Empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on fourteen real networks show that the gravity model and the local gravity model perform very competitively in comparison with well-known state-of-the-art methods. For the local gravity model, the empirical results suggest an approximately linear relation between the optimal truncation radius and the average distance of the network.Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information, innovations, behaviors, and so on. Inspired by the gravity law, we propose a gravity model that utilizes both neighborhood information and path information to measure a node's importance in spreading dynamics. In order to reduce the accumulated errors caused by interactions at distance and to lower the computational complexity, a local version of the gravity model is further proposed by introducing a truncation radius. Empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on fourteen real networks show that the gravity model and the local gravity model perform very competitively in comparison with well-known state-of-the-art methods. For the local gravity model, the empirical results suggest an approximately linear relation between the optimal truncation radius and the average distance of the network.
ArticleNumber 8387
Author Zhang, Yixin
Li, Zhe
Ren, Tao
Zhou, Tao
Ma, Xiaoqi
Liu, Simiao
Author_xml – sequence: 1
  givenname: Zhe
  surname: Li
  fullname: Li, Zhe
  organization: Software College, Northeastern University of China
– sequence: 2
  givenname: Tao
  surname: Ren
  fullname: Ren, Tao
  email: chinarentao@163.com
  organization: Software College, Northeastern University of China
– sequence: 3
  givenname: Xiaoqi
  orcidid: 0000-0003-0074-4192
  surname: Ma
  fullname: Ma, Xiaoqi
  organization: School of Science and Technology, Nottingham Trent University
– sequence: 4
  givenname: Simiao
  surname: Liu
  fullname: Liu, Simiao
  organization: Software College, Northeastern University of China
– sequence: 5
  givenname: Yixin
  surname: Zhang
  fullname: Zhang, Yixin
  organization: Software College, Northeastern University of China
– sequence: 6
  givenname: Tao
  surname: Zhou
  fullname: Zhou, Tao
  email: zhutou@ustc.edu
  organization: CompleX Lab, University of Electronic Science and Technology of China
BackLink https://www.ncbi.nlm.nih.gov/pubmed/31182773$$D View this record in MEDLINE/PubMed
BookMark eNp9kctOAyEYhYmp8VJ9ARdmEjduRrkPbEyM8dLExI2uCcxAxUyHCjNN-vZS66W6KBsgfOfk_JxDMOpCZwE4QfACQSIuE0VMihIiWVIqCSzlDjjAkLISE4xHG-d9cJzSG8yLYUmR3AP7BCGBq4ocADxpbNd7t_TdtPCda4fVVbdFmkerGxtTYZbFNOqF75fFLDS2PQK7TrfJHn_tY_Byd_t881A-Pt1Pbq4fy5pR2JfGNRA729TYEMk5qgk1psLEQYONMIxraZFjRmpOXWMR18xljhooBWqgJGNwtfadD2aWfXKwqFs1j36m41IF7dXfl86_qmlYKM5YJRjMBudfBjG8Dzb1auZTbdtWdzYMSWFMGa8ElTSjZ__QtzDELo-XKVIJjqqKZ-p0M9FPlO_vzIBYA3UMKUXrVO173fuwCuhbhaBalafW5alcnvosT62mxf-k3-5bRWQtym3lAm38jb1F9QFQfawF
CitedBy_id crossref_primary_10_1088_1674_1056_ac4226
crossref_primary_10_1109_TCSS_2021_3073899
crossref_primary_10_3390_electronics13203992
crossref_primary_10_1016_j_chaos_2022_112120
crossref_primary_10_1109_ACCESS_2022_3213332
crossref_primary_10_2478_jaiscr_2023_0013
crossref_primary_10_3390_app14209599
crossref_primary_10_1109_TCYB_2021_3123081
crossref_primary_10_1016_j_ress_2024_110488
crossref_primary_10_1007_s11042_023_17025_x
crossref_primary_10_1016_j_jbusres_2024_114869
crossref_primary_10_1088_1742_5468_abe2a1
crossref_primary_10_1016_j_eswa_2023_121154
crossref_primary_10_1177_01423312231182468
crossref_primary_10_1016_j_chaos_2022_112998
crossref_primary_10_3233_JIFS_191899
crossref_primary_10_1016_j_future_2023_05_026
crossref_primary_10_1016_j_omega_2023_102945
crossref_primary_10_1080_23307706_2023_2176935
crossref_primary_10_1063_1_5141153
crossref_primary_10_1016_j_physa_2022_126879
crossref_primary_10_1016_j_chaos_2025_116299
crossref_primary_10_1142_S0129183119500931
crossref_primary_10_1038_s41598_023_43585_x
crossref_primary_10_1016_j_ins_2024_121067
crossref_primary_10_1016_j_chaos_2024_115227
crossref_primary_10_17798_bitlisfen_1407941
crossref_primary_10_1016_j_ememar_2024_101138
crossref_primary_10_3390_math10060970
crossref_primary_10_1016_j_physa_2022_127117
crossref_primary_10_1088_1742_5468_adb4cd
crossref_primary_10_1016_j_comcom_2023_11_003
crossref_primary_10_1038_s41598_025_93387_6
crossref_primary_10_3390_app14020521
crossref_primary_10_1088_1742_5468_acdceb
crossref_primary_10_1016_j_chaos_2024_114487
crossref_primary_10_1016_j_ins_2023_01_097
crossref_primary_10_1016_j_jclepro_2023_138859
crossref_primary_10_1209_0295_5075_ad7884
crossref_primary_10_1016_j_chaos_2024_114924
crossref_primary_10_1142_S0219525923500091
crossref_primary_10_7498_aps_71_20220565
crossref_primary_10_1007_s10489_023_04457_z
crossref_primary_10_1016_j_jocs_2024_102473
crossref_primary_10_1088_1674_1056_ab77fe
crossref_primary_10_1371_journal_pone_0251208
crossref_primary_10_3390_math11061302
crossref_primary_10_1007_s12043_024_02864_6
crossref_primary_10_1016_j_knosys_2024_111580
crossref_primary_10_1093_comjnl_bxad097
crossref_primary_10_1016_j_physa_2021_126479
crossref_primary_10_1016_j_eswa_2024_126292
crossref_primary_10_1088_1674_1056_aca6d8
crossref_primary_10_1016_j_frl_2023_104225
crossref_primary_10_1007_s10115_024_02262_9
crossref_primary_10_1007_s42524_022_0190_8
crossref_primary_10_1016_j_ins_2021_08_026
crossref_primary_10_1016_j_jksuci_2023_101906
crossref_primary_10_1016_j_eswa_2020_113681
crossref_primary_10_7498_aps_72_20221878
crossref_primary_10_1007_s13278_024_01232_x
crossref_primary_10_3390_su13052687
crossref_primary_10_3390_math8091449
crossref_primary_10_1016_j_chaos_2024_115675
crossref_primary_10_1016_j_chaos_2024_115159
crossref_primary_10_1016_j_ins_2022_10_070
crossref_primary_10_1038_s41598_021_01218_1
crossref_primary_10_1109_TCSS_2023_3295177
crossref_primary_10_1016_j_eswa_2023_122171
crossref_primary_10_1088_1367_2630_ad0e89
crossref_primary_10_3390_math9202531
crossref_primary_10_3390_a18010006
crossref_primary_10_1063_5_0127434
crossref_primary_10_1080_13504851_2024_2339375
crossref_primary_10_1109_JETCAS_2023_3283680
crossref_primary_10_1109_ACCESS_2023_3268797
crossref_primary_10_1016_j_eswa_2019_113092
crossref_primary_10_1016_j_ress_2024_110384
crossref_primary_10_1109_TETCI_2024_3372410
crossref_primary_10_3389_fcvm_2021_755321
crossref_primary_10_1088_1674_1056_ad20d6
crossref_primary_10_1093_comnet_cnae015
crossref_primary_10_1038_s41598_022_14005_3
crossref_primary_10_1016_j_physa_2022_127797
crossref_primary_10_7498_aps_69_20191686
crossref_primary_10_1109_ACCESS_2020_2985713
crossref_primary_10_3390_e27030298
crossref_primary_10_1016_j_knosys_2019_105464
crossref_primary_10_3389_fphy_2023_1239660
crossref_primary_10_3934_math_2025106
crossref_primary_10_1016_j_physa_2025_130518
crossref_primary_10_1155_2023_6985650
crossref_primary_10_1016_j_physa_2022_128353
crossref_primary_10_1016_j_physa_2023_129188
crossref_primary_10_1016_j_physa_2024_130237
crossref_primary_10_1109_TNSE_2022_3208343
crossref_primary_10_1142_S0217984923500768
crossref_primary_10_1142_S0217979221501836
crossref_primary_10_3390_e22040450
crossref_primary_10_1016_j_chaos_2025_116078
crossref_primary_10_3390_sym12010100
crossref_primary_10_1016_j_chaos_2024_115400
crossref_primary_10_1103_PhysRevResearch_4_033105
crossref_primary_10_1109_ACCESS_2024_3363635
crossref_primary_10_1016_j_chaos_2021_110934
Cites_doi 10.1145/1134271.1134277
10.1080/0022250X.1972.9989806
10.1145/1772690.1772756
10.1103/PhysRevE.74.036104
10.1038/srep00292
10.1038/srep05097
10.1371/journal.pcbi.1001109
10.1103/PhysRevLett.89.208701
10.1080/15427951.2009.10129177
10.1140/epjb/e2008-00370-y
10.1016/j.physa.2008.01.113
10.1103/PhysRevE.69.025103
10.1016/S0169-7552(98)00110-X
10.1103/PhysRevE.65.036104
10.1371/journal.pone.0021202
10.1137/S0036144500371907
10.1038/ncomms10168
10.1145/367766.368168
10.1142/S0219525903001067
10.1016/j.pharmthera.2013.01.016
10.1016/0378-8733(78)90021-7
10.1109/TNET.2003.822655
10.1038/30918
10.1073/pnas.0507655102
10.1016/j.physrep.2016.06.007
10.1016/j.physa.2015.12.162
10.1073/pnas.200327197
10.2307/3033543
10.1103/PhysRevE.68.065103
10.1038/nature14604
10.1038/nphys1746
10.1145/1217299.1217301
10.1093/oso/9780198805090.001.0001
10.1016/j.physa.2011.09.017
10.1093/biomet/30.1-2.81
10.1093/acprof:oso/9780199211517.001.0001
10.1103/PhysRevLett.105.218701
10.1056/NEJMsa066082
10.1038/nature04153
10.1145/3097983.3098069
10.1038/srep21380
ContentType Journal Article
Copyright The Author(s) 2019
The Author(s) 2019. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: The Author(s) 2019
– notice: The Author(s) 2019. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID C6C
AAYXX
CITATION
NPM
3V.
7X7
7XB
88A
88E
88I
8FE
8FH
8FI
8FJ
8FK
ABUWG
AEUYN
AFKRA
AZQEC
BBNVY
BENPR
BHPHI
CCPQU
DWQXO
FYUFA
GHDGH
GNUQQ
HCIFZ
K9.
LK8
M0S
M1P
M2P
M7P
PHGZM
PHGZT
PIMPY
PJZUB
PKEHL
PPXIY
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
Q9U
7X8
5PM
DOI 10.1038/s41598-019-44930-9
DatabaseName Springer Nature OA Free Journals
CrossRef
PubMed
ProQuest Central (Corporate)
Health & Medical Collection
ProQuest Central (purchase pre-March 2016)
Biology Database (Alumni Edition)
Medical Database (Alumni Edition)
Science Database (Alumni Edition)
ProQuest SciTech Collection
ProQuest Natural Science Journals
ProQuest Hospital Collection
Hospital Premium Collection (Alumni Edition)
ProQuest Central (Alumni) (purchase pre-March 2016)
ProQuest Central (Alumni)
ProQuest One Sustainability (subscription)
ProQuest Central UK/Ireland
ProQuest Central Essentials
Biological Science Collection
ProQuest Central
Natural Science Collection
ProQuest One Community College
ProQuest Central Korea
Health Research Premium Collection
Health Research Premium Collection (Alumni)
ProQuest Central Student
SciTech Premium Collection
ProQuest Health & Medical Complete (Alumni)
Biological Sciences
Health & Medical Collection (Alumni)
Medical Database
Science Database
Biological Science Database
ProQuest Central Premium
ProQuest One Academic
ProQuest Publicly Available Content
ProQuest Health & Medical Research Collection
ProQuest One Academic Middle East (New)
ProQuest One Health & Nursing
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
ProQuest Central Basic
MEDLINE - Academic
PubMed Central (Full Participant titles)
DatabaseTitle CrossRef
PubMed
Publicly Available Content Database
ProQuest Central Student
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest Health & Medical Complete (Alumni)
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest One Health & Nursing
ProQuest Natural Science Collection
ProQuest Central China
ProQuest Biology Journals (Alumni Edition)
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest One Sustainability
ProQuest Health & Medical Research Collection
Health Research Premium Collection
Health and Medicine Complete (Alumni Edition)
Natural Science Collection
ProQuest Central Korea
Health & Medical Research Collection
Biological Science Collection
ProQuest Central (New)
ProQuest Medical Library (Alumni)
ProQuest Science Journals (Alumni Edition)
ProQuest Biological Science Collection
ProQuest Central Basic
ProQuest Science Journals
ProQuest One Academic Eastern Edition
ProQuest Hospital Collection
Health Research Premium Collection (Alumni)
Biological Science Database
ProQuest SciTech Collection
ProQuest Hospital Collection (Alumni)
ProQuest Health & Medical Complete
ProQuest Medical Library
ProQuest One Academic UKI Edition
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
MEDLINE - Academic
DatabaseTitleList CrossRef


Publicly Available Content Database
MEDLINE - Academic
PubMed
Database_xml – sequence: 1
  dbid: C6C
  name: Springer Nature OA Free Journals
  url: http://www.springeropen.com/
  sourceTypes: Publisher
– sequence: 2
  dbid: NPM
  name: PubMed
  url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed
  sourceTypes: Index Database
– sequence: 3
  dbid: BENPR
  name: ProQuest Central
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Biology
EISSN 2045-2322
ExternalDocumentID PMC6557850
31182773
10_1038_s41598_019_44930_9
Genre Research Support, Non-U.S. Gov't
Journal Article
GrantInformation_xml – fundername: Funder: National Natural Science Foundation of China Grant Reference Number: 61473073 Funder: National Natural Science Foundation of China Grant Reference Number: 61104074 Funder: Fundamental Research Funds for the Central Universities Grant Reference Number: N161702001 Funder: Program for Liaoning Excellent Talents in University Grant Reference Number: LJQ2014028
– fundername: National Natural Science Foundation of China (National Science Foundation of China)
  grantid: 61433014
  funderid: https://doi.org/10.13039/501100001809
– fundername: ;
– fundername: ;
  grantid: 61433014
GroupedDBID 0R~
3V.
4.4
53G
5VS
7X7
88A
88E
88I
8FE
8FH
8FI
8FJ
AAFWJ
AAJSJ
AAKDD
ABDBF
ABUWG
ACGFS
ACSMW
ACUHS
ADBBV
ADRAZ
AENEX
AEUYN
AFKRA
AJTQC
ALIPV
ALMA_UNASSIGNED_HOLDINGS
AOIJS
AZQEC
BAWUL
BBNVY
BCNDV
BENPR
BHPHI
BPHCQ
BVXVI
C6C
CCPQU
DIK
DWQXO
EBD
EBLON
EBS
EJD
ESX
FYUFA
GNUQQ
GROUPED_DOAJ
GX1
HCIFZ
HH5
HMCUK
HYE
KQ8
LK8
M0L
M1P
M2P
M48
M7P
M~E
NAO
OK1
PIMPY
PQQKQ
PROAC
PSQYO
RNT
RNTTT
RPM
SNYQT
UKHRP
AASML
AAYXX
AFPKN
CITATION
PHGZM
PHGZT
NPM
PJZUB
PPXIY
PQGLB
7XB
8FK
AARCD
K9.
PKEHL
PQEST
PQUKI
PRINS
Q9U
7X8
5PM
ID FETCH-LOGICAL-c540t-bfd02fedc2b39661c34bb723f0b2b8b56a9e1f5b9a64fde16a5f9664b0981d093
IEDL.DBID 7X7
ISSN 2045-2322
IngestDate Thu Aug 21 13:52:21 EDT 2025
Fri Jul 11 15:53:41 EDT 2025
Wed Aug 13 04:04:22 EDT 2025
Mon Jul 21 05:41:01 EDT 2025
Tue Jul 01 03:08:50 EDT 2025
Thu Apr 24 23:02:31 EDT 2025
Fri Feb 21 02:39:09 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
License Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c540t-bfd02fedc2b39661c34bb723f0b2b8b56a9e1f5b9a64fde16a5f9664b0981d093
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ORCID 0000-0003-0074-4192
OpenAccessLink https://www.proquest.com/docview/2237861776?pq-origsite=%requestingapplication%
PMID 31182773
PQID 2237861776
PQPubID 2041939
ParticipantIDs pubmedcentral_primary_oai_pubmedcentral_nih_gov_6557850
proquest_miscellaneous_2245678494
proquest_journals_2237861776
pubmed_primary_31182773
crossref_citationtrail_10_1038_s41598_019_44930_9
crossref_primary_10_1038_s41598_019_44930_9
springer_journals_10_1038_s41598_019_44930_9
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2019-06-10
PublicationDateYYYYMMDD 2019-06-10
PublicationDate_xml – month: 06
  year: 2019
  text: 2019-06-10
  day: 10
PublicationDecade 2010
PublicationPlace London
PublicationPlace_xml – name: London
– name: England
PublicationTitle Scientific reports
PublicationTitleAbbrev Sci Rep
PublicationTitleAlternate Sci Rep
PublicationYear 2019
Publisher Nature Publishing Group UK
Nature Publishing Group
Publisher_xml – name: Nature Publishing Group UK
– name: Nature Publishing Group
References HuHBWangXFUnified index to quantifying heterogeneity of complex networksPhysica A2008387376937802008PhyA..387.3769H10.1016/j.physa.2008.01.113
KendallMA new measure of rank correlationBiometrika193830818910.1093/biomet/30.1-2.81
LüLZhouTZhangQMStanleyHEThe H-index of a network node and its relation to degree and corenessNat. Commun.201672016NatCo...710168L10.1038/ncomms10168
McauleyJJLeskovecJLearning to discover social circles in ego networksAdv. Neural Inf. Process. Syst.201225548556
WangWAsymmetrically interacting spreading dynamics on complex layered networksSci. Rep.201441:CAS:528:DC%2BC2MXktlOgsLk%3D10.1038/srep05097
LüLZhangYCYeungCHZhouTLeaders in social networks, the delicious casePLoS One20116e212022011PLoSO...621202L10.1371/journal.pone.0021202
CsermelyPKorcsmárosTKissHJLondonGNussinovRStructure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive reviewPharmacol. Ther.20131383334081:CAS:528:DC%2BC3sXls1CgtLk%3D10.1016/j.pharmthera.2013.01.016
KitsakMIdentification of influential spreaders in complex networksNat. Phys.201068888931:CAS:528:DC%2BC3cXhtlKltLfL10.1038/nphys1746
YanXYZhouTDestination ChoiceGame: A Spatial Interaction Theory on Human MobilityNatural Resources20182234239
Yin, H., Austin, R., Benson, J. L. & David, F. G. Local higher-order graph clustering. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 555–564 (ACM Press, 2017).
GuimerȧRDanonLDíaz-GuileraAGiraltFArenasASelf-similar community structure in a network of human interactionsPhys. Rev. E2003680651032003PhRvE..68f5103G10.1103/PhysRevE.68.065103
WattsDJStrogatzSHCollective dynamics of ‘small-world’ networksNature19983934404421998Natur.393..440W1:CAS:528:DyaK1cXjs1Khsrk%3D10.1038/30918
NewmanMEJFinding community structure in networks using the eigenvectors of matricesPhys. Rev. E2006740361042006PhRvE..74c6104N22821391:STN:280:DC%2BD28rpslahuw%3D%3D10.1103/PhysRevE.74.036104
SpringNMahajanRWetherallDAndersonTMeasuring ISP topologies with rocketfuelIEEE/ACM Trans. Networking20041221610.1109/TNET.2003.822655
GleiserPDanonLCommunity structure in JazzAdv. Complex Syst.2003656510.1142/S0219525903001067
LiuJGLinJHGuoQZhouTLocating influential nodes via dynamics-sensitive centralitySci. Rep.201662016NatSR...621380L1:CAS:528:DC%2BC28Xjt1emurc%3D10.1038/srep21380
Pastor-SatorrasRVespignaniAImmunization of complex networksPhys. Rev. E2002650361042002PhRvE..65c6104P10.1103/PhysRevE.65.036104
CastellanoCPastor-SatorrasRThresholds for epidemic spreading in networksPhys. Rev. Lett.20101052187012010PhRvL.105u8701C10.1103/PhysRevLett.105.218701
BonacichPFactoring and weighting approaches to status scores and clique identificationMath. Sociol.1972211312010.1080/0022250X.1972.9989806
LeskovecJLangKJDasguptaAMahoneyMWCommunity structure in large networks: natural cluster sizes and the absence of large well-defined clustersInternet Math.2009629123273609010.1080/15427951.2009.10129177
FreemanLCA set of measures of centrality based on betweennessSociometry197740354110.2307/3033543
Adamic, L. A. & Glance, N. The political blogosphere and the 2004 U.S. election: divided they blog. In Proceedings of the 3rd international workshop on Link discovery. 36–43 (ACM Press, 2005).
FloydRWAlgorithm 97: shortest pathCommun. ACM1962534510.1145/367766.368168
MaLLMaCZhangHFWangBHIdentifying influential spreaders in complex networks based on gravity formulaPhysica A20154512052122016PhyA..451..205M10.1016/j.physa.2015.12.162
Batageli, V. & Mrvar, A. Pajek Datasets. Available at, http://vlado.fmf.uni-lj.si/pub/networks/data/ (2007).
YanGFuZQChenGEpidemic threshold and phase transition in scale-free networks with asymmetric infectionEur. Phys. J. B2008655915942008EPJB...65..591Y1:CAS:528:DC%2BD1cXhsVCjtbrM10.1140/epjb/e2008-00370-y
MoroneFMakseHAInfluence maximization in complex networks through optimal percolationNature201552465682015Natur.524...65M1:CAS:528:DC%2BC2MXhtFyltL%2FL10.1038/nature14604
FreemanLCCentrality in social networks conceptual clarificationSoc. Networks1979121523910.1016/0378-8733(78)90021-7
LeskovecJKleinbergJFaloutsosCGraph evolution: densification and shrinking diametersACM Trans. Knowl. Discov. Data20071210.1145/1217299.1217301
HethcoteHWThe mathematics of infectious diseasesSIAM Rev.2009425996532000SIAMR..42..599H181404910.1137/S0036144500371907
RochaLELiljerosFHolmePSimulated epidemics in an empirical spatiotemporal network of 50,185 sexual contactsPLoS Comput. Biol.20117e10011092011PLSCB...7E1109R1:CAS:528:DC%2BC3MXktVWhtLc%3D10.1371/journal.pcbi.1001109
ChristakisNAFowlerJHThe spread of obesity in a large social network over 32 yearsN. Engl. J. Med.20073573703791:CAS:528:DC%2BD2sXotFChtb0%3D10.1056/NEJMsa066082
AmaralLANScalaABarthelemyMStanleyHEClasses of small-world networksPNAS20009711149111522000PNAS...9711149A1:CAS:528:DC%2BD3cXnsF2rt7g%3D10.1073/pnas.200327197
Caldarelli, G. Scale-Free Networks: Complex Webs in Nature and Technology (Oxford University Press, Oxford, 2007).
Newman, M. E. J. Networks (Oxford University Press, Oxford, 2018).
LüLVital nodes identification in complex networksPhys. Rep.20166501632016PhR...650....1L354385710.1016/j.physrep.2016.06.007
Lloyd-SmithJOSchreiberSJKoppPEGetzWMSuperspreading and the effect of individual variation on disease emergenceNature20054383553592005Natur.438..355L1:CAS:528:DC%2BD2MXht1WksbbE10.1038/nature04153
HirschJEAn index to quantify an individual’s scientific research outputProc. Natl. Acad. Sci. USA200510216569165722005PNAS..10216569H1:CAS:528:DC%2BD2MXht1Kgs7fL10.1073/pnas.0507655102
NewmanMEJAssortative mixing in networksPhys. Rev. Lett.2002892087012002PhRvL..89t8701N1:STN:280:DC%2BD38notleksA%3D%3D10.1103/PhysRevLett.89.208701
AlbertRAlbertINakaradoGLStructural vulnerability of the North American power gridPhys. Rev. E2004690251032004PhRvE..69b5103A10.1103/PhysRevE.69.025103
BrinSPageLThe anatomy of a large-scale hypertextual web search engineComput. Netw. ISDN Syst.19983010711710.1016/S0169-7552(98)00110-X
KlemmKSerranoMÁEguíluzVMSan MiguelMA measure of individual role in collective dynamicsSci. Rep.2012210.1038/srep00292
Leskovec, J., Huttenlocher, D. & Kleinberg, J. Predicting positive and negative links in online social networks. In Proceedings of the 19th international conference on World Wide Web. 641–650 (ACM Press, 2010).
ChenDLüLShangMSZhangYCZhouTIdentifying influential nodes in complex networksPhysica A2012391177717872012PhyA..391.1777C10.1016/j.physa.2011.09.017
44930_CR30
J Leskovec (44930_CR25) 2009; 6
44930_CR2
LC Freeman (44930_CR15) 1977; 40
P Gleiser (44930_CR20) 2003; 6
44930_CR1
S Brin (44930_CR12) 1998; 30
J Leskovec (44930_CR22) 2007; 1
P Bonacich (44930_CR9) 1972; 2
G Yan (44930_CR42) 2008; 65
DJ Watts (44930_CR31) 1998; 393
F Morone (44930_CR5) 2015; 524
P Csermely (44930_CR7) 2013; 138
C Castellano (44930_CR35) 2010; 105
HB Hu (44930_CR34) 2008; 387
NA Christakis (44930_CR17) 2007; 357
LL Ma (44930_CR16) 2015; 451
JG Liu (44930_CR41) 2016; 6
44930_CR26
JE Hirsch (44930_CR44) 2005; 102
L Lü (44930_CR13) 2011; 6
44930_CR28
R Pastor-Satorras (44930_CR4) 2002; 65
44930_CR23
L Lü (44930_CR8) 2016; 650
K Klemm (44930_CR40) 2012; 2
JO Lloyd-Smith (44930_CR3) 2005; 438
MEJ Newman (44930_CR33) 2002; 89
LAN Amaral (44930_CR38) 2000; 97
W Wang (44930_CR43) 2014; 4
LC Freeman (44930_CR14) 1979; 1
M Kitsak (44930_CR11) 2010; 6
N Spring (44930_CR32) 2004; 12
L Lü (44930_CR10) 2016; 7
MEJ Newman (44930_CR21) 2006; 74
D Chen (44930_CR19) 2012; 391
JJ Mcauley (44930_CR27) 2012; 25
XY Yan (44930_CR39) 2018; 2
RW Floyd (44930_CR18) 1962; 5
HW Hethcote (44930_CR36) 2009; 42
R Guimerȧ (44930_CR24) 2003; 68
LE Rocha (44930_CR29) 2011; 7
M Kendall (44930_CR37) 1938; 30
R Albert (44930_CR6) 2004; 69
References_xml – reference: NewmanMEJAssortative mixing in networksPhys. Rev. Lett.2002892087012002PhRvL..89t8701N1:STN:280:DC%2BD38notleksA%3D%3D10.1103/PhysRevLett.89.208701
– reference: YanGFuZQChenGEpidemic threshold and phase transition in scale-free networks with asymmetric infectionEur. Phys. J. B2008655915942008EPJB...65..591Y1:CAS:528:DC%2BD1cXhsVCjtbrM10.1140/epjb/e2008-00370-y
– reference: RochaLELiljerosFHolmePSimulated epidemics in an empirical spatiotemporal network of 50,185 sexual contactsPLoS Comput. Biol.20117e10011092011PLSCB...7E1109R1:CAS:528:DC%2BC3MXktVWhtLc%3D10.1371/journal.pcbi.1001109
– reference: YanXYZhouTDestination ChoiceGame: A Spatial Interaction Theory on Human MobilityNatural Resources20182234239
– reference: LiuJGLinJHGuoQZhouTLocating influential nodes via dynamics-sensitive centralitySci. Rep.201662016NatSR...621380L1:CAS:528:DC%2BC28Xjt1emurc%3D10.1038/srep21380
– reference: HuHBWangXFUnified index to quantifying heterogeneity of complex networksPhysica A2008387376937802008PhyA..387.3769H10.1016/j.physa.2008.01.113
– reference: Newman, M. E. J. Networks (Oxford University Press, Oxford, 2018).
– reference: Caldarelli, G. Scale-Free Networks: Complex Webs in Nature and Technology (Oxford University Press, Oxford, 2007).
– reference: KitsakMIdentification of influential spreaders in complex networksNat. Phys.201068888931:CAS:528:DC%2BC3cXhtlKltLfL10.1038/nphys1746
– reference: BrinSPageLThe anatomy of a large-scale hypertextual web search engineComput. Netw. ISDN Syst.19983010711710.1016/S0169-7552(98)00110-X
– reference: LüLZhouTZhangQMStanleyHEThe H-index of a network node and its relation to degree and corenessNat. Commun.201672016NatCo...710168L10.1038/ncomms10168
– reference: Batageli, V. & Mrvar, A. Pajek Datasets. Available at, http://vlado.fmf.uni-lj.si/pub/networks/data/ (2007).
– reference: WattsDJStrogatzSHCollective dynamics of ‘small-world’ networksNature19983934404421998Natur.393..440W1:CAS:528:DyaK1cXjs1Khsrk%3D10.1038/30918
– reference: CastellanoCPastor-SatorrasRThresholds for epidemic spreading in networksPhys. Rev. Lett.20101052187012010PhRvL.105u8701C10.1103/PhysRevLett.105.218701
– reference: FreemanLCCentrality in social networks conceptual clarificationSoc. Networks1979121523910.1016/0378-8733(78)90021-7
– reference: HethcoteHWThe mathematics of infectious diseasesSIAM Rev.2009425996532000SIAMR..42..599H181404910.1137/S0036144500371907
– reference: MaLLMaCZhangHFWangBHIdentifying influential spreaders in complex networks based on gravity formulaPhysica A20154512052122016PhyA..451..205M10.1016/j.physa.2015.12.162
– reference: GleiserPDanonLCommunity structure in JazzAdv. Complex Syst.2003656510.1142/S0219525903001067
– reference: LüLZhangYCYeungCHZhouTLeaders in social networks, the delicious casePLoS One20116e212022011PLoSO...621202L10.1371/journal.pone.0021202
– reference: Yin, H., Austin, R., Benson, J. L. & David, F. G. Local higher-order graph clustering. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 555–564 (ACM Press, 2017).
– reference: Adamic, L. A. & Glance, N. The political blogosphere and the 2004 U.S. election: divided they blog. In Proceedings of the 3rd international workshop on Link discovery. 36–43 (ACM Press, 2005).
– reference: Pastor-SatorrasRVespignaniAImmunization of complex networksPhys. Rev. E2002650361042002PhRvE..65c6104P10.1103/PhysRevE.65.036104
– reference: HirschJEAn index to quantify an individual’s scientific research outputProc. Natl. Acad. Sci. USA200510216569165722005PNAS..10216569H1:CAS:528:DC%2BD2MXht1Kgs7fL10.1073/pnas.0507655102
– reference: WangWAsymmetrically interacting spreading dynamics on complex layered networksSci. Rep.201441:CAS:528:DC%2BC2MXktlOgsLk%3D10.1038/srep05097
– reference: Lloyd-SmithJOSchreiberSJKoppPEGetzWMSuperspreading and the effect of individual variation on disease emergenceNature20054383553592005Natur.438..355L1:CAS:528:DC%2BD2MXht1WksbbE10.1038/nature04153
– reference: LeskovecJLangKJDasguptaAMahoneyMWCommunity structure in large networks: natural cluster sizes and the absence of large well-defined clustersInternet Math.2009629123273609010.1080/15427951.2009.10129177
– reference: AlbertRAlbertINakaradoGLStructural vulnerability of the North American power gridPhys. Rev. E2004690251032004PhRvE..69b5103A10.1103/PhysRevE.69.025103
– reference: FloydRWAlgorithm 97: shortest pathCommun. ACM1962534510.1145/367766.368168
– reference: GuimerȧRDanonLDíaz-GuileraAGiraltFArenasASelf-similar community structure in a network of human interactionsPhys. Rev. E2003680651032003PhRvE..68f5103G10.1103/PhysRevE.68.065103
– reference: LüLVital nodes identification in complex networksPhys. Rep.20166501632016PhR...650....1L354385710.1016/j.physrep.2016.06.007
– reference: FreemanLCA set of measures of centrality based on betweennessSociometry197740354110.2307/3033543
– reference: LeskovecJKleinbergJFaloutsosCGraph evolution: densification and shrinking diametersACM Trans. Knowl. Discov. Data20071210.1145/1217299.1217301
– reference: KendallMA new measure of rank correlationBiometrika193830818910.1093/biomet/30.1-2.81
– reference: BonacichPFactoring and weighting approaches to status scores and clique identificationMath. Sociol.1972211312010.1080/0022250X.1972.9989806
– reference: NewmanMEJFinding community structure in networks using the eigenvectors of matricesPhys. Rev. E2006740361042006PhRvE..74c6104N22821391:STN:280:DC%2BD28rpslahuw%3D%3D10.1103/PhysRevE.74.036104
– reference: ChenDLüLShangMSZhangYCZhouTIdentifying influential nodes in complex networksPhysica A2012391177717872012PhyA..391.1777C10.1016/j.physa.2011.09.017
– reference: McauleyJJLeskovecJLearning to discover social circles in ego networksAdv. Neural Inf. Process. Syst.201225548556
– reference: KlemmKSerranoMÁEguíluzVMSan MiguelMA measure of individual role in collective dynamicsSci. Rep.2012210.1038/srep00292
– reference: CsermelyPKorcsmárosTKissHJLondonGNussinovRStructure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive reviewPharmacol. Ther.20131383334081:CAS:528:DC%2BC3sXls1CgtLk%3D10.1016/j.pharmthera.2013.01.016
– reference: MoroneFMakseHAInfluence maximization in complex networks through optimal percolationNature201552465682015Natur.524...65M1:CAS:528:DC%2BC2MXhtFyltL%2FL10.1038/nature14604
– reference: SpringNMahajanRWetherallDAndersonTMeasuring ISP topologies with rocketfuelIEEE/ACM Trans. Networking20041221610.1109/TNET.2003.822655
– reference: ChristakisNAFowlerJHThe spread of obesity in a large social network over 32 yearsN. Engl. J. Med.20073573703791:CAS:528:DC%2BD2sXotFChtb0%3D10.1056/NEJMsa066082
– reference: Leskovec, J., Huttenlocher, D. & Kleinberg, J. Predicting positive and negative links in online social networks. In Proceedings of the 19th international conference on World Wide Web. 641–650 (ACM Press, 2010).
– reference: AmaralLANScalaABarthelemyMStanleyHEClasses of small-world networksPNAS20009711149111522000PNAS...9711149A1:CAS:528:DC%2BD3cXnsF2rt7g%3D10.1073/pnas.200327197
– ident: 44930_CR26
  doi: 10.1145/1134271.1134277
– volume: 2
  start-page: 113
  year: 1972
  ident: 44930_CR9
  publication-title: Math. Sociol.
  doi: 10.1080/0022250X.1972.9989806
– ident: 44930_CR28
  doi: 10.1145/1772690.1772756
– volume: 74
  start-page: 036104
  year: 2006
  ident: 44930_CR21
  publication-title: Phys. Rev. E
  doi: 10.1103/PhysRevE.74.036104
– volume: 2
  year: 2012
  ident: 44930_CR40
  publication-title: Sci. Rep.
  doi: 10.1038/srep00292
– volume: 4
  year: 2014
  ident: 44930_CR43
  publication-title: Sci. Rep.
  doi: 10.1038/srep05097
– volume: 7
  start-page: e1001109
  year: 2011
  ident: 44930_CR29
  publication-title: PLoS Comput. Biol.
  doi: 10.1371/journal.pcbi.1001109
– volume: 89
  start-page: 208701
  year: 2002
  ident: 44930_CR33
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.89.208701
– volume: 2
  start-page: 234
  year: 2018
  ident: 44930_CR39
  publication-title: Natural Resources
– volume: 6
  start-page: 29
  year: 2009
  ident: 44930_CR25
  publication-title: Internet Math.
  doi: 10.1080/15427951.2009.10129177
– volume: 65
  start-page: 591
  year: 2008
  ident: 44930_CR42
  publication-title: Eur. Phys. J. B
  doi: 10.1140/epjb/e2008-00370-y
– volume: 387
  start-page: 3769
  year: 2008
  ident: 44930_CR34
  publication-title: Physica A
  doi: 10.1016/j.physa.2008.01.113
– volume: 69
  start-page: 025103
  year: 2004
  ident: 44930_CR6
  publication-title: Phys. Rev. E
  doi: 10.1103/PhysRevE.69.025103
– volume: 30
  start-page: 107
  year: 1998
  ident: 44930_CR12
  publication-title: Comput. Netw. ISDN Syst.
  doi: 10.1016/S0169-7552(98)00110-X
– volume: 65
  start-page: 036104
  year: 2002
  ident: 44930_CR4
  publication-title: Phys. Rev. E
  doi: 10.1103/PhysRevE.65.036104
– volume: 6
  start-page: e21202
  year: 2011
  ident: 44930_CR13
  publication-title: PLoS One
  doi: 10.1371/journal.pone.0021202
– volume: 42
  start-page: 599
  year: 2009
  ident: 44930_CR36
  publication-title: SIAM Rev.
  doi: 10.1137/S0036144500371907
– volume: 7
  year: 2016
  ident: 44930_CR10
  publication-title: Nat. Commun.
  doi: 10.1038/ncomms10168
– volume: 5
  start-page: 345
  year: 1962
  ident: 44930_CR18
  publication-title: Commun. ACM
  doi: 10.1145/367766.368168
– volume: 6
  start-page: 565
  year: 2003
  ident: 44930_CR20
  publication-title: Adv. Complex Syst.
  doi: 10.1142/S0219525903001067
– volume: 138
  start-page: 333
  year: 2013
  ident: 44930_CR7
  publication-title: Pharmacol. Ther.
  doi: 10.1016/j.pharmthera.2013.01.016
– volume: 1
  start-page: 215
  year: 1979
  ident: 44930_CR14
  publication-title: Soc. Networks
  doi: 10.1016/0378-8733(78)90021-7
– volume: 12
  start-page: 2
  year: 2004
  ident: 44930_CR32
  publication-title: IEEE/ACM Trans. Networking
  doi: 10.1109/TNET.2003.822655
– volume: 393
  start-page: 440
  year: 1998
  ident: 44930_CR31
  publication-title: Nature
  doi: 10.1038/30918
– volume: 102
  start-page: 16569
  year: 2005
  ident: 44930_CR44
  publication-title: Proc. Natl. Acad. Sci. USA
  doi: 10.1073/pnas.0507655102
– volume: 650
  start-page: 1
  year: 2016
  ident: 44930_CR8
  publication-title: Phys. Rep.
  doi: 10.1016/j.physrep.2016.06.007
– volume: 451
  start-page: 205
  year: 2015
  ident: 44930_CR16
  publication-title: Physica A
  doi: 10.1016/j.physa.2015.12.162
– volume: 97
  start-page: 11149
  year: 2000
  ident: 44930_CR38
  publication-title: PNAS
  doi: 10.1073/pnas.200327197
– volume: 40
  start-page: 35
  year: 1977
  ident: 44930_CR15
  publication-title: Sociometry
  doi: 10.2307/3033543
– volume: 68
  start-page: 065103
  year: 2003
  ident: 44930_CR24
  publication-title: Phys. Rev. E
  doi: 10.1103/PhysRevE.68.065103
– volume: 524
  start-page: 65
  year: 2015
  ident: 44930_CR5
  publication-title: Nature
  doi: 10.1038/nature14604
– volume: 6
  start-page: 888
  year: 2010
  ident: 44930_CR11
  publication-title: Nat. Phys.
  doi: 10.1038/nphys1746
– volume: 1
  start-page: 2
  year: 2007
  ident: 44930_CR22
  publication-title: ACM Trans. Knowl. Discov. Data
  doi: 10.1145/1217299.1217301
– ident: 44930_CR1
  doi: 10.1093/oso/9780198805090.001.0001
– volume: 391
  start-page: 1777
  year: 2012
  ident: 44930_CR19
  publication-title: Physica A
  doi: 10.1016/j.physa.2011.09.017
– volume: 25
  start-page: 548
  year: 2012
  ident: 44930_CR27
  publication-title: Adv. Neural Inf. Process. Syst.
– ident: 44930_CR30
– volume: 30
  start-page: 81
  year: 1938
  ident: 44930_CR37
  publication-title: Biometrika
  doi: 10.1093/biomet/30.1-2.81
– ident: 44930_CR2
  doi: 10.1093/acprof:oso/9780199211517.001.0001
– volume: 105
  start-page: 218701
  year: 2010
  ident: 44930_CR35
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.105.218701
– volume: 357
  start-page: 370
  year: 2007
  ident: 44930_CR17
  publication-title: N. Engl. J. Med.
  doi: 10.1056/NEJMsa066082
– volume: 438
  start-page: 355
  year: 2005
  ident: 44930_CR3
  publication-title: Nature
  doi: 10.1038/nature04153
– ident: 44930_CR23
  doi: 10.1145/3097983.3098069
– volume: 6
  year: 2016
  ident: 44930_CR41
  publication-title: Sci. Rep.
  doi: 10.1038/srep21380
SSID ssj0000529419
Score 2.638086
Snippet Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information,...
SourceID pubmedcentral
proquest
pubmed
crossref
springer
SourceType Open Access Repository
Aggregation Database
Index Database
Enrichment Source
Publisher
StartPage 8387
SubjectTerms 639/766/530/2801
639/766/530/2804
Algorithms
Collaboration
Computer applications
Epidemics
Gravity
Humanities and Social Sciences
Influence
Information processing
multidisciplinary
Neighborhoods
Science
Science (multidisciplinary)
Social networks
Spreading
SummonAdditionalLinks – databaseName: Scholars Portal Journals: Open Access
  dbid: M48
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1bS8MwFD7MieCLeLc6pYJvWk2btEkeREQcQ5hPDnwLzZqgMOplG7h_70nTTubtuSdtci6cL03O-QBObEZYbmJnAWFcSY7GmBM0GqY6tTyzcZG7_5D9-6w3YHeP6WMLGrqjWoHjX7d2jk9q8D46_3ibXWHAX_qScXExxiTkCsViGTEmKYnkEixjZuIuUPs13Pe9vhPJYlnXzvw-dDE__QCdP-9OfjtArfJSdx3WakAZXnsP2ICWKTdhxVNMzrYg8ZW4VTVT-OwZSTCoRyG-z99iDvUsdCRECMfDihdnGwbd24ebXlTzJKBGGZlE2hYksTilRFPcvcRDyrTmCbVEJ1roNMuliW2qZZ4xW5g4y1OLckwTiWiVSLoD7fKlNHsQFsZKI6RIBTGM60JYyzixQ4x86_Y-AcSNdtSwbiLuuCxGqjrMpkJ5jSrUqKo0qmQAp_Mxr76Fxr_SnUbpqvEGhRiGC8RaHCdwPH-MgeBON_LSvEydDGJBLphkAex6G80_R902inMaAF-w3lzANdlefFI-P1XNtrPUtQMiAZw1dv6a1t-r2P9_FQewmjifcxxIpAPtyfvUHCK4meijymM_ARNt9KU
  priority: 102
  providerName: Scholars Portal
– databaseName: Springer Nature OA Free Journals
  dbid: C6C
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8QwEB5WRfAivq2uUsGbFtMmbZKjLIoIenJhb6XZJriwdEXXg__emfQh66rgOZM2nUfzJfMCOHcZE4WNSQLKUkqOQZtTPBqnJnUyc3FZ0D3kw2N2NxT3o3TUg6TNhfFB-76kpf9Nt9FhV2-40VAyWKwjITRnkV6BNSrdTlo9yAbdvQp5rkSsm_wYxtUPUxf3oCVguRwf-c1J6vee2y3YbEBjeF0vcxt6ttqB9bqN5McuJHW2rc9YCid11xE03GmIz6sjlUPzEVKjIYTcoe99swfD25unwV3U9EJArgk2j4wrWeJwSYnheEKJx1wYIxPumEmMMmlWaBu71OgiE660cVakDumEYRoRKdN8H1arWWUPISyt01ZplSpmhTSlck5I5sZo3Y7ONwHELXfycVMonPpVTHPvsOYqrzmaI0dzz9FcB3DRzXmpy2T8Sd1vmZ43JvOWI06RCvGUxAWcdcOo7OTBKCo7eycaxHtSCS0COKhl1L2O01FJSh6AXJBeR0CFtBdHqsmzL6idpVTyhwVw2cr5a1m_f8XR_8iPYSMhHaS-R6wPq_PXd3uCgGZuTr0GfwKLx-9K
  priority: 102
  providerName: Springer Nature
Title Identifying influential spreaders by gravity model
URI https://link.springer.com/article/10.1038/s41598-019-44930-9
https://www.ncbi.nlm.nih.gov/pubmed/31182773
https://www.proquest.com/docview/2237861776
https://www.proquest.com/docview/2245678494
https://pubmed.ncbi.nlm.nih.gov/PMC6557850
Volume 9
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3dS-QwEB_uVg7uRbxPq97Sg3vTYtqk-XiSdVFkQRE_YN9K0yacIF1114f9751Ju5U9OV9aaNI2mUkyk5nM_AD-eMlE6VLigHYUkmNxzmmeVLnNvZI-rUuyQ55fyLNbMZnm087gNu-OVa7WxLBQ17OKbOSHKMaURnGr5NHDY0KoUeRd7SA0PsIGpS6jI11qqnobC3mxRGq6WBnG9eEc5RXFlKUmEcJwlph1efRGyXx7VvIfh2mQQ6dbsNkpkPGo5fgX-OCar_CphZRcfoOsjbwN0UvxXYtAgpP4PsbvtaeWY7uMCXQI1e844OB8h9vTk5vxWdLhIiAFBVsk1tcs89ikzHLcraQVF9aqjHtmM6ttLkvjUp9bU0rha5fKMvdYT1hmUDtlhv-AQTNr3DbEtfPGaaNzzZxQttbeC8V8hTPd014ngnRFnaLqkoYTdsV9EZzXXBctRQukaBEoWpgI9vt3HtqUGe_W3lsRveimz7x4ZXYEv_tiHPjkzSgbN3umOqj7KS2MiOBny6P-d5y2TUrxCNQa9_oKlFR7vaS5-xuSa8uc0v-wCA5WfH5t1v97sfN-L3bhc0ZjjjCP2B4MFk_P7hcqMws7DCN2CBuj0eR6gvfjk4vLK3w6luNhMBDg9VzoFynP90Y
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3dT9wwDLfQoWl7mdh3B2ydtD1tFWmTNsnDhPYBOgacpgkk3rKmTTQk1APu0HT_1P7G2U1bdEPjjee4TWs7thPH_gG89QUTpUtJAspRSY7FNad4UuU297LwaV3SOeThpBgfi28n-ckK_OlrYehaZW8TW0NdTys6I99CNyYVultZbJ9fJIQaRdnVHkIjqMW-W_zGLdvs495XlO-7LNvdOfoyTjpUAZxfsHlifc0y7-oqsxxj_bTiwlqZcc9sZpXNi1K71OdWl4XwtUuLMvdIJyzTGNu1zZfQ5K8KjluZEax-3pl8_zGc6lDeTKS6q85hXG3N0ENSFVuqEyE0Z4le9oA3wtqbtzP_SdG2nm93DR52IWv8KejYI1hxzWO4F0AsF08gC7W-bb1UfBowT9BsnMX4vnBPOraLmGCOMOCPW-Sdp3B8Jzx7BqNm2rgXENfOa6e0yhVzQtpaeS8k8xXaFk-7qwjSnjum6tqUE1rGmWnT5VyZwFGDHDUtR42O4P3wzHlo0nEr9UbPdNMt2Jm5Vq8I3gzDuNQof1I2bnpFNBhtSiW0iOB5kNEwHaeNmpQ8ArkkvYGA2ngvjzSnv9p23kVODYdYBB96OV9_1v__4uXtf_Ea7o-PDg_Mwd5kfx0eZKR_hLjENmA0v7xymxhKze2rTn9j-HnXS-YvPF0wog
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwEB5VRSAuiDeBUoIEJ4jWju3YPiBUtaxaChUHKu0txIktKlXZwm6F9q_x65hxHtW2oree4yT2vO3xzAfwJhRMVp4TB4ynkhyHOmdEViungi4Cbyo6h_x6VOwfy88zNduAv0MtDF2rHGxiNNTNvKYz8gm6MW3Q3epiEvprEd_2ph_PfmWEIEWZ1gFOoxORQ7_6g9u3xYeDPeT12zyffvq-u5_1CAM4F8mWmQsNy4Nv6twJjPt5LaRzOheBudwZp4rKeh6Us1UhQ-N5UamA46RjFuO82IgJzf8tLRQnHdMzPZ7vUAZNctvX6TBhJgv0lVTPxm0mpRUss-u-8EqAe_We5qVkbfSB0_twrw9e051O2h7Ahm8fwu0OznL1CPKu6jdWTqUnHfoJGpDTFL_X3ZhO3SolwCMM_dOIwfMYjm-EYk9gs523_hmkjQ_WG2uUYV5q15gQpGahRisTaJ-VAB-oU9Z9w3LCzTgtY-JcmLKjaIkULSNFS5vAu_Gds65dx7Wjtwail73qLsoLQUvg9fgYlY4yKVXr5-c0BuNObaSVCTzteDT-TtCWTWuRgF7j3jiAGnqvP2lPfsbG3oWi1kMsgfcDny-m9f9VPL9-Fa_gDipK-eXg6PAF3M1J_Ah6iW3B5vL3uX-JMdXSbUfhTeHHTWvLPxrZM3I
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Identifying+influential+spreaders+by+gravity+model&rft.jtitle=Scientific+reports&rft.au=Li%2C+Zhe&rft.au=Ren%2C+Tao&rft.au=Ma%2C+Xiaoqi&rft.au=Liu+Simiao&rft.date=2019-06-10&rft.pub=Nature+Publishing+Group&rft.eissn=2045-2322&rft.volume=9&rft.issue=1&rft_id=info:doi/10.1038%2Fs41598-019-44930-9&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2045-2322&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2045-2322&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2045-2322&client=summon