Skip to main content

Impact of Global Edge-Removal on the Average Path Length

  • Conference paper
  • 806 Accesses

Abstract

In this paper, we further explore into the impact of link removal from a global point of view. While diseases spread more efficiently through the best spreaders and removal of local links attached to them can have great impact, it is also important to have a method to estimate the cost of edge-removal from a global point of view since the removal of a link may also affect certain global properties of the network. We discuss global strategies on link removal and study their effectiveness in controlling the propagation of infectious diseases based on the spreading control characteristics (SCC). The SCC framework opens up a comprehensive way for researchers to assess and compare the efficacy of their strategies against the potential cost of their implementation from a global perspective.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hufnagel, L., Brockman, D., Geisel, T.: Forecast and control of epidemics in a globalized world. Proc. Natl. Acad. Sci. USA 101, 15124–15129 (2004)

    Article  Google Scholar 

  2. Brownstein, J.S., Wolfe, C.J., Mandl, K.D.: Empirical evidence for the effect of airline travel on inter-regional influenza spread in the United States. Plos. Medicine 3, 1826–1835 (2006)

    Google Scholar 

  3. Holme, P., Kim, B.J., Yoon, C.N., Han, S.K.: Attack vulnerability of complex networks. Phys. Rev. E 65, 056109 (2002)

    Google Scholar 

  4. Pastor-Satorras, R., Vespignani, A.: Immunization of complex networks. Phys. Rev. E 65, 036104 (2002)

    Google Scholar 

  5. Marcelino, J., Kaiser, M.: Reducing influenza spreading over the airline network. PLOS Currents, RRN1005 (2009)

    Google Scholar 

  6. Kitsak, M., Gallos, L.K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H.E., Makse, H.A.: Identification of influential spreaders in complex networks. Nature Phys. 6, 888–893 (2010)

    Article  Google Scholar 

  7. Zhou, J., Liu, Z.: Epidemic spreading in communities with mobile agents. Physica A 388, 1228–1236 (2009)

    Article  Google Scholar 

  8. Chen, Y., Paul, G., Havlin, S., Liljeros, F., Stanley, H.E.: Finding a better immunization strategies. Phys. Rev. Lett. 101, 058701 (2008)

    Google Scholar 

  9. Colizza, V., Barrat, A., Barthélemy, M., Vespignani, A.: The role of the airline transportation network in the prediction and predictability of global epidemics. Proc. Natl. Acad. Sci. USA 103, 2015–2020 (2006)

    Article  MATH  Google Scholar 

  10. Newman, M.E.J.: Spread of epidemic disease on networks. Phys. Rev. E 66, 016128 (2002)

    Google Scholar 

  11. Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001)

    Article  Google Scholar 

  12. Lessler, J., Kaufman, J.H., Ford, D.A., Douglas, J.V.: The cost of simplifying air travel when modeling disease spread. Plos One 4, e4403 (2009)

    Google Scholar 

  13. Crépey, P., Barthélemy, M.: Detecting robust patterns in the spread of epidemics: A case study of influenza in the United States and France. Am. J. Epidemiol. 166, 1244–1251 (2007)

    Article  Google Scholar 

  14. Chung, N.N., Chew, L.Y., Zhou, J., Lai, C.H.: Impact of edge removal on the centrality of the best spreaders. Europhys. Lett. 98, 58004 (2012)

    Article  Google Scholar 

  15. Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A 357, 593–612 (2005)

    Article  Google Scholar 

  16. Colizza, V., Pastor-Satorras, R., Vespignani, A.: Reaction-diffusion processes and metapopulation models in heterogeneous networks. Nature Physics 3, 276–282 (2007)

    Article  Google Scholar 

  17. Jones, B.: Computational Geometry Database (February 2002), http://compgeom.cs.edu/~jeffe/compgeom/biblios.html

  18. Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: densification and shrinking diameters. ACM Transactions on Knowledge Discovery from Data (ACM TKDD) 1(1) (2007)

    Google Scholar 

  19. Ripeanu, M., Foster, I., Iamnitchi, A.: Mapping the Gnutella Network: Properties of Large-Scale Peer-to-Peer Systems and Implications for System Design. IEEE Internet Computing Journal (2002)

    Google Scholar 

  20. Newman, M.E.J.: Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Phys. Rev. E 64, 016132 (2001)

    Google Scholar 

  21. Seidman, S.B.: Network structure and minimum degree. Social Networks 5, 269–287 (1983)

    Article  MathSciNet  Google Scholar 

  22. Carmi, S., Havlin, S., Kirkpatrick, S., Shavitt, Y., Shir, E.A.: A model of internet topology using k-shell decomposition. Proc. Natl. Acad. Sci. USA 104, 11150–11154 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering

About this paper

Cite this paper

Chew, L.Y., Chung, N.N., Zhou, J., Lai, C.H. (2013). Impact of Global Edge-Removal on the Average Path Length. In: Glass, K., Colbaugh, R., Ormerod, P., Tsao, J. (eds) Complex Sciences. Complex 2012. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-03473-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03473-7_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03472-0

  • Online ISBN: 978-3-319-03473-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics