Identification of influential spreaders in complex networks (original) (raw)

Nature Physics volume 6, pages 888–893 (2010)Cite this article

Abstract

Networks portray a multitude of interactions through which people meet, ideas are spread and infectious diseases propagate within a society1,2,3,4,5. Identifying the most efficient ‘spreaders’ in a network is an important step towards optimizing the use of available resources and ensuring the more efficient spread of information. Here we show that, in contrast to common belief, there are plausible circumstances where the best spreaders do not correspond to the most highly connected or the most central people6,7,8,9,10. Instead, we find that the most efficient spreaders are those located within the core of the network as identified by the _k_-shell decomposition analysis11,12,13, and that when multiple spreaders are considered simultaneously the distance between them becomes the crucial parameter that determines the extent of the spreading. Furthermore, we show that infections persist in the high-k shells of the network in the case where recovered individuals do not develop immunity. Our analysis should provide a route for an optimal design of efficient dissemination strategies.

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References

  1. Caldarelli, G. & Vespignani, A. (eds) Large Scale Structure and Dynamics of Complex Networks (World Scientific, 2007).
  2. Anderson, R. M., May, R. M. & Anderson, B. Infectious Diseases of Humans: Dynamics and Control (Oxford Science Publications, 1992).
    Google Scholar
  3. Diekmann, O. & Heesterbeek, J. A. P. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation (Wiley Series in Mathematical & Computational Biology, 2000).
    MATH Google Scholar
  4. Keeling, M. J. & Rohani, P. Modeling Infectious Diseases in Humans and Animals (Princeton Univ. Press, 2008).
    MATH Google Scholar
  5. Rogers, E. M. Diffusion of Innovation 4th edn (Free Press, 1995).
    Google Scholar
  6. Albert, R., Jeong, H. & Barabási, A-L. Error and attack tolerance of complex networks. Nature 406, 378–482 (2000).
    Article ADS Google Scholar
  7. Pastor-Satorras, R. & Vespignani, A. Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001).
    Article ADS Google Scholar
  8. Cohen, R., Erez, K., ben-Avraham, D. & Havlin, S. Breakdown of the Internet under intentional attack. Phys. Rev. Lett. 86, 3682–3685 (2001).
    Article ADS Google Scholar
  9. Freeman, L. C. Centrality in social networks: Conceptual clarification. Social Networks 1, 215–239 (1979).
    Article Google Scholar
  10. Friedkin, N. E. Theoretical foundations for centrality measures. Am. J. Sociology 96, 1478–1504 (1991).
    Article Google Scholar
  11. Bollobás, B. Graph Theory and Combinatorics: Proceedings of the Cambridge Combinatorial Conference in Honor of P. Erdös Vol. 35 (Academic, 1984).
    Google Scholar
  12. Seidman, S. B. Network structure and minimum degree. Social Networks 5, 269–287 (1983).
    Article MathSciNet Google Scholar
  13. Carmi, S., Havlin, S, Kirkpatrick, S., Shavitt, Y. & Shir, E. A model of Internet topology using k-shell decomposition. Proc. Natl Acad. Sci. USA 104, 11150–11154 (2007).
    Article ADS Google Scholar
  14. Ángeles-Serrano, M. & Boguñá, M. Clustering in complex networks. II. Percolation properties. Phys. Rev. E 74, 056116 (2006).
    Article MathSciNet Google Scholar
  15. LiveJournal, http://www.livejournal.com.
  16. Liljeros, F., Giesecke, J. & Holme, P. The contact network of inpatients in a regional healthcare system. A longitudinal case study. Math. Population Studies 14, 269–284 (2007).
    Article MathSciNet Google Scholar
  17. The Internet Movie Database, http://www.imdb.com.
  18. Hethcote, H. W. The mathematics of infectious diseases. SIAM Rev. 42, 599–653 (2000).
    Article ADS MathSciNet Google Scholar
  19. Castellano, C., Fortunato, S. & Loretto, V. Statistical Physics of Social Dynamics. Rev. Mod. Phys. 81, 591–646 (2009).
    Article ADS Google Scholar
  20. Shavitt, Y. & Shir, E. DIMES: Let the internet measure itself. ACM SIGCOMM Comput. Commun. Rev. 35, 71–74 (2005).
    Article Google Scholar
  21. Molloy, M. & Reed, B. A critical point for random graphs with a given degree sequence. Random Struct. Algorithms 6, 161–180 (1995).
    Article MathSciNet Google Scholar
  22. Hidalgo, C. A., Klinger, B., Barabasi, A-L. & Hausmann, R. The product space conditions the development of nations. Science 317, 482–487 (2007).
    Article ADS Google Scholar
  23. Hethcote, H. & Rogers, J. A. Gonorrhea Transmission Dynamics and Control (Springer-Verlag, 1984).
    Book Google Scholar
  24. Pastor-Satorras, R. & Vespignani, A. Immunization of complex networks. Phys. Rev. E 65, 036104 (2002).
    Article ADS Google Scholar
  25. Dezsó, Z. & Barabási, A-L. Halting viruses in scale-free networks. Phys. Rev. E 65, 055103 (2002).
    Article ADS Google Scholar
  26. Cohen, R., Erez, K., ben-Avraham, D. & Havlin, S. Resilience of the Internet to random breakdowns. Phys. Rev. Lett. 85, 4626–4630 (2000).
    Article ADS Google Scholar
  27. Newman, M. E. J. Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002).
    Article ADS Google Scholar
  28. Large Network visualization tool, http://xavier.informatics.indiana.edu/lanet-vi/.
  29. Alvarez-Hamelin, J. I., Dallásta, L., Barrat, A. & Vespignani, A. Large scale networks fingerprinting and visualization using the k-core decomposition. Adv. Neural Inform. Process. Systems 18, 41–51 (2006).
    Google Scholar

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Acknowledgements

We thank NSF-SES, NSF-EF, ONR, DTRA, Epiwork and the Israel Science Foundation for support. F.L. is supported by Riksbankens Jubileumsfond. We thank L. Braunstein, J. Brujić, kc claffy, D. Krioukov and C. Song for discussions and S. Zhou for providing the email dataset. The use of the hospital dataset was approved by the Regional Ethical Review Board in Stockholm (Record 2004=5:8).

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Authors and Affiliations

  1. Center for Polymer Studies and Physics Department, Boston University, Boston, Massachusetts 02215, USA
    Maksim Kitsak & H. Eugene Stanley
  2. Cooperative Association for Internet Data Analysis (CAIDA), University of California-San Diego, La Jolla, California 92093, USA
    Maksim Kitsak
  3. Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA
    Lazaros K. Gallos & Hernán A. Makse
  4. Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan, Israel
    Shlomo Havlin
  5. Department of Sociology, Stockholm University, Stockholm, S-10691, Sweden
    Fredrik Liljeros
  6. Operations and Management Sciences Department, Information, Stern School of Business, New York University, New York, New York 10012, USA
    Lev Muchnik

Authors

  1. Maksim Kitsak
  2. Lazaros K. Gallos
  3. Shlomo Havlin
  4. Fredrik Liljeros
  5. Lev Muchnik
  6. H. Eugene Stanley
  7. Hernán A. Makse

Contributions

All authors contributed equally to the work presented in this paper.

Corresponding author

Correspondence toHernán A. Makse.

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Competing interests

The authors declare no competing financial interests.

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Kitsak, M., Gallos, L., Havlin, S. et al. Identification of influential spreaders in complex networks.Nature Phys 6, 888–893 (2010). https://doi.org/10.1038/nphys1746

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