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Competition-Induced Preferential Attachment

  • N. Berger
  • C. Borgs
  • J. T. Chayes
  • R. M. D’Souza
  • R. D. Kleinberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an explanation of how it can arise from a more basic underlying mechanism of competition between opposing forces.

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics. This family admits an equivalent description as a graph process with no reference to the underlying geometry. Moreover, the resulting graph process is shown to be preferential attachment with an upper cutoff. We rigorously determine the degree distribution for the family of random graph models, showing that it obeys a power law up to a finite threshold and decays exponentially above this threshold.

We also introduce and rigorously analyze a generalized version of our graph process, with two natural parameters, one corresponding to the cutoff and the other a “fertility” parameter. Limiting cases of this process include the standard preferential attachment model (introduced by Price and by Barabási-Albert) and the uniform attachment model. In the general case, we prove that the process has a power law degree distribution up to a cutoff, and establish monotonicity of the power as a function of the two parameters.

Keywords

Degree Distribution Preferential Attachment Degree Sequence Random Graph Model Attachment Model 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • N. Berger
    • 1
  • C. Borgs
    • 1
  • J. T. Chayes
    • 1
  • R. M. D’Souza
    • 1
  • R. D. Kleinberg
    • 2
  1. 1.Microsoft ResearchRedmondUSA
  2. 2.Supported by a Fannie and John Hertz Foundation FellowshipM.I.T. CSAILCambridgeUSA

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