The European Physical Journal Special Topics

, Volume 223, Issue 13, pp 2745–2758 | Cite as

The clash of the Titans: How preferential attachment helps the survival of the smallest

  • S. Aich
  • A. Mehta
Part of the following topical collections:
  1. Advanced Computational and Experimental Techniques in Nolinear Dynamics. Guest Editors: Elbert E.N. Macau and Carlos L. Pando Lambruschini (Eds.)


We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and indefinite growth of clusters which are isolated from each other. The presence of preferential attachment results in an inhomogeneous topology, where hubs monopolise the connections, while most other nodes are sparsely connected. Interestingly, this results in the protection of the less massive clusters from annihilation, to which the hubs are doomed.


European Physical Journal Special Topic Eventual Survivor Degree Distribution Preferential Attachment Massive Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra Systems (World Scientific, Singapore, 1996)Google Scholar
  2. 2.
    R.E. Michod, Darwinian Dynamics: Evolutionary Transitions in Fitness and Individuality (Princeton University Press, 2000)Google Scholar
  3. 3.
    A.S. Ackleh, D.F. Marshall, B.G. Fitzpatrick, H.E. Heatherly, Math. Models Methods Appl. Sci. 9, 1379 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    T.M. Massie, B. Blasius, G. Weithoff, U. Gaedke, G.F. Fussmannc, Proc. Natl. Acad. Sci. 107, 4236 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    A. Mehta, A.S. Majumdar, J.M. Luck, edited by A. Chatterjee, et al. Econophysics of Wealth Distributions (Springer-Verlag, Italia, 2005)Google Scholar
  6. 6.
    J.M. Luck, A. Mehta, Eur. Phys. J. B 44, 79 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    N.N. Thyagu, A. Mehta, Physica A 390, 1458 (2011)Google Scholar
  8. 8.
    R. Albert, H. Jeong, A.L. Barabási, Nature (London) 401, 130 (1999)ADSCrossRefGoogle Scholar
  9. 9.
    R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002)ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    M. Faloutsos, P. Faloutsos, C. Faloutsos, Comput. Commun. Rev. 29, 251 (1999)CrossRefGoogle Scholar
  11. 11.
    A.L. Barabási, R. Albert, Science 286, 509 (1999)ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    R. Albert, A.L. Barabási, Phys. Rev. Lett. 85, 5234 (2000)ADSCrossRefGoogle Scholar
  13. 13.
    L.A.N. Amaral, A. Scala, M. Barthélémy, H.E. Stanley, Proc. Natl. Acad. Sci. USA 97, 11149 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    M.E.J. Newman, Proc. Natl. Acad. Sci. USA 98, 404 (2001)ADSCrossRefMathSciNetzbMATHGoogle Scholar
  15. 15.
    M.E.J. Newman, Phys. Rev. E 64, 016131 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    M.E.J. Newman, Phys. Rev. E 64, 016132 (2001)ADSCrossRefGoogle Scholar
  17. 17.
    H. Jeong, S.P. Mason, Z.N. Oltvai, A.L. Barabási, Nature (London) 411, 41 (2001)ADSCrossRefGoogle Scholar
  18. 18.
    R.J. Williams, N.D. Martinez, E.L. Berlow, J.A. Dunne, A.L. Barabási, Proc. Natl. Acad. Sci. 99, 12913 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    A.L. Barabási, H. Jeong, E. Ravasz, Z. Néda, A. Schubert, T. Vicsek, Physica A 311, 590 (2002)Google Scholar
  20. 20.
    P. Erdös, A. Rényi, Publ. Math. (Debrecen) 6, 290 (1959)MathSciNetzbMATHGoogle Scholar
  21. 21.
    P. Erdös, A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960)zbMATHGoogle Scholar
  22. 22.
    P. Erdös, A. Rényi, Bull. Inst. Int. Stat. 38, 343 (1961)zbMATHGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Department of Theoretical SciencesSatyendra Nath Bose National Centre for Basic SciencesKolkataIndia

Personalised recommendations