Degree Distribution of the FKP Network Model

  • Noam Berger
  • Béla Bollobás
  • Christian Borgs
  • Jennifer Chayes
  • Oliver Riordan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)

Abstract

Recently, Fabrikant, Koutsoupias and Papadimitriou [7] introduced a natural and beautifully simple model of network growth involving a trade-off between geometric and network objectives, with relative strength characterized by a single parameter which scales as a power of the number of nodes. In addition to giving experimental results, they proved a power-law lower bound on part of the degree sequence, for a wide range of scalings of the parameter. Here we prove that, despite the FKP results, the overall degree distribution is very far from satisfying a power law.

First, we establish that for almost all scalings of the parameter, either all but a vanishingly small fraction of the nodes have degree 1, or there is exponential decay of node degrees. In the former case, a power law can hold for only a vanishingly small fraction of the nodes. Furthermore, we show that in this case there is a large number of nodes with almost maximum degree. So a power law fails to hold even approximately at either end of the degree range. Thus the power laws found in [7] are very different from those given by other internet models or found experimentally [8].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Noam Berger
    • 1
  • Béla Bollobás
    • 2
    • 3
    • 5
  • Christian Borgs
    • 4
  • Jennifer Chayes
    • 4
  • Oliver Riordan
    • 3
    • 5
  1. 1.Department of StatisticsUniversity of CaliforniaBerkeley
  2. 2.Department of Mathematical SciencesUniversity of MemphisMemphis
  3. 3.Trinity CollegeCambridgeUK
  4. 4.Microsoft ResearchRedmond
  5. 5.Department of Pure MathematicsCambridge

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