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Discontinuous Explosive Percolation with Multiple Giant Components

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Explosive Percolation in Random Networks

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Abstract

The percolation phase transition models the onset of large-scale connectivity in lattices or networks, in systems ranging from porous media, to resistor networks, to epidemic spreading [1–4].

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References

  1. Stauffer, D., Aharony, A.: Introduction to Percolation Theory. Taylor & Francis, London (1994)

    Google Scholar 

  2. Sahimi, M.: Applications of Percolation Theory. Taylor & Francis, London (1994)

    Google Scholar 

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

    Article  Google Scholar 

  4. Moore, C., Newman, M.E.J.: Epidemics and percolation in small-world networks. Phys. Rev. E 61, 5678–5682 (2000)

    Article  Google Scholar 

  5. Achlioptas, D., D’Souza, R.M., Spencer. J.: Explosive percolation in random networks. Science 323, 1453–1455 (2009)

    Google Scholar 

  6. Cho, Y.S., Kim, J.S., Park, J.: Kahng, B, Kim, D.: Percolation transitions in scale-free networks under the Achlioptas process. Phys. Rev. Lett. 103, 135702 (2009)

    Google Scholar 

  7. Radicchi, F., Fortunato, S.: Explosive percolation in scale-free networks. Phys. Rev. Lett. 103, 168701 (2009)

    Article  Google Scholar 

  8. Ziff, R.M.: Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks. Phys. Rev. Lett. 103, 045701 (2009)

    Article  Google Scholar 

  9. Ziff, R.M.: Scaling behavior of explosive percolation on the square lattice. Phys. Rev. E 82, 051105 (2010)

    Article  Google Scholar 

  10. D’Souza, R.M., Mitzenmacher, M.: Local cluster aggregation models of explosive percolation. Phys. Rev. Lett. 104, 195702 (2010)

    Article  Google Scholar 

  11. Cho, Y.S., Kahng, B., Kim, D.: Cluster aggregation model for discontinuous percolation transitions. Phys. Rev. E 81, 030103(R) (2010)

    Article  Google Scholar 

  12. Manna, S.S., Chatterjee, A.: A new route to explosive percolation. Phys. A 390, 177–182 (2011)

    Article  Google Scholar 

  13. AraĂşjo, N.A.M., Herrmann, H.J.: Explosive percolation via control of the largest cluster. Phys. Rev. Lett. 105, 035701 (2010)

    Article  Google Scholar 

  14. Friedman, E.J., Landsberg, A.S.: Construction and analysis of random networks with explosive percolation. Phys. Rev. Lett. 103, 255701 (2009)

    Article  Google Scholar 

  15. Nagler, J., Levina, A., Timme, M.: Impact of single links in competitive percolation. Nature Phys. 7, 265–270 (2011)

    Article  Google Scholar 

  16. Rozenfeld, H.D., Gallos, L.K., Makse, H.A.: Explosive percolation in the human protein homology network. Eur. Phys. J. B 75, 305–310 (2010)

    Article  MATH  Google Scholar 

  17. Bohman, T., Frieze, A., Wormald, N.C.: Avoidance of a giant component in half the edge set of a random graph. Random Struct. Algorithms 25, 432–449 (2004)

    Article  MathSciNet  Google Scholar 

  18. Spencer, J.: The giant component: The golden anniversary. Not. AMS 57, 720–724 (2010)

    MATH  Google Scholar 

  19. Erdös, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17 (1960)

    MATH  Google Scholar 

  20. Ben-Naim, E., Krapivsky, P.L.: Percolation with multiple giant clusters. J. Phys. A 38, L417–L423 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. da Costa, R.A., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F.: Explosive percolation transition is actually continuous. Phys. Rev. Lett. 105, 255701 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Peking University, Beijing, China

    Wei Chen

Authors
  1. Wei Chen
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Correspondence to Wei Chen .

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Chen, W. (2014). Discontinuous Explosive Percolation with Multiple Giant Components. In: Explosive Percolation in Random Networks. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43739-1_2

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