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A stochastic evolutionary model exhibiting power-law behaviour with an exponential cutoff

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  • Fenner, Trevor
  • Levene, Mark
  • Loizou, George

Abstract

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the “rich get richer” phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein and e-mail networks. Such networks may in fact exhibit an exponential cutoff in the power-law scaling, although this cutoff may only be observable in the tail of the distribution for extremely large networks. We propose a modification of the basic stochastic evolutionary model, so that after a node is chosen preferentially, say according to the number of its inlinks, there is a small probability that this node will be discarded. We show that as a result of this modification, by viewing the stochastic process in terms of an urn transfer model, we obtain a power-law distribution with an exponential cutoff. Unlike many other models, the current model can capture instances where the exponent of the distribution is less than or equal to two. As a proof of concept, we demonstrate the consistency of our model by analysing a yeast protein interaction network, the distribution of which is known to follow a power law with an exponential cutoff.

Suggested Citation

  • Fenner, Trevor & Levene, Mark & Loizou, George, 2005. "A stochastic evolutionary model exhibiting power-law behaviour with an exponential cutoff," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 641-656.
  • Handle: RePEc:eee:phsmap:v:355:y:2005:i:2:p:641-656
    DOI: 10.1016/j.physa.2005.01.007
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    References listed on IDEAS

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    1. S. Redner, 1998. "How popular is your paper? An empirical study of the citation distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 4(2), pages 131-134, July.
    2. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
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    1. Fenner, Trevor & Levene, Mark & Loizou, George, 2010. "Predicting the long tail of book sales: Unearthing the power-law exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2416-2421.
    2. Zörnig, Peter, 2010. "Statistical simulation and the distribution of distances between identical elements in a random sequence," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2317-2327, October.

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