A Geometric Preferential Attachment Model of Networks II

  • Abraham D. Flaxman
  • Alan M. Frieze
  • Juan Vera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4863)


A detailed understanding of expansion in complex networks can greatly aid in the design and analysis of algorithms for a variety of important network tasks, including routing messages, ranking nodes, and compressing graphs. This has motivated several recent investigations of expansion properties in real-world graphs and also in random models of real-world graphs, like the preferential attachment graph. The results point to a gap between real-world observations and theoretical models. Some real-world graphs are expanders and others are not, but a graph generated by the preferential attachment model is an expander whp .

We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with power-law degree distribution where the expansion property depends on a tunable parameter of the model.

The vertices of Gn are n sequentially generated points x1,x2,...,xn chosen uniformly at random from the unit sphere in Open image in new window. After generating xt, we randomly connect it to m points from those points in x1,x2,...,xt − 1 ....


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Abraham D. Flaxman
    • 1
  • Alan M. Frieze
    • 1
  • Juan Vera
    • 1
  1. 1.Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213U.S.A.

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