Location of Repository

A model for collaboration networks giving rise to a power law distribution with exponential cutoff

By Trevor Fenner, Mark Levene and George Loizou

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, e-mail, actor and collaboration 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 become inactive. 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 empirically by analysing the Mathematical Research collaboration network, the distribution of which is known to follow a power law with an exponential cutoff

Topics: csis
Publisher: Elsevier
Year: 2007
OAI identifier: oai:eprints.bbk.ac.uk.oai2:281

Suggested articles

Preview

Citations

  1. (2005). A stochastic evolutionary model exhibiting power-law behaviour with an exponential cutoff. doi
  2. (2005). A stochastic model for the evolution of the web allowing link deletion. doi
  3. (2002). A stochastic model for the evolution of the Web. doi
  4. (2000). Classes of small-world networks.
  5. (2000). Connectivity of growing random networks. doi
  6. (2000). Critical Phenomema in the Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools. Springer Series in Synergetics. doi
  7. (1999). Emergence of scaling in random networks. doi
  8. (2000). Error and attack tolerance of complex networks. doi
  9. (1842). Evolution of networks with aging of sites. Physical Review E, doi
  10. (2000). Graph structure in the Web. doi
  11. (1998). How popular is your paper? An empirical study of the citation distribution. doi
  12. (1983). Introduction to Stochastic Dynamic Programming. doi
  13. (2001). Lethality and centrality in protein networks.
  14. (1999). Mean-field theory for scale free random networks. doi
  15. (1955). On a class of skew distribution functions. doi
  16. (2002). Patterns of collaboration in mathematical research.
  17. (2004). Problem with fitting to the power-law distribution. doi
  18. (2002). Scale-free topology of e-mail networks. Physical Review E, doi
  19. (0461). Search in powerlaw networks. Physical Review E, doi
  20. (2002). Statistical mechanics of complex networks.
  21. (2000). Stochastic models for the web graph. doi
  22. (2001). The structure of scientific collaboration networks. doi
  23. (2001). Towards compressing web graphs. doi
  24. (2002). Truncation power law behavior in “scale-free” network models due to information filtering. Physical Review Letters, doi
  25. (2002). Winners don’t take all: Characterizing the competition for links on the web. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.