Degree distribution of the FKP network model

  • Authors:
  • Noam Berger;Béla Bollobás;Christian Borgs;Jennifer Chayes;Oliver Riordan

  • Affiliations:
  • Department of Statistics, University of California, Berkeley, CA;Department of Mathematical Sciences, University of Memphis, Memphis, TN and Trinity College, UK and Royal Society research fellow, Department of Pure Mathematics, Cambridge;Microsoft Research, Redmond, WA;Microsoft Research, Redmond, WA;Trinity College, UK and Royal Society research fellow, Department of Pure Mathematics, Cambridge

  • Venue:
  • ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
  • Year:
  • 2003

Quantified Score

Hi-index 0.00

Visualization

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].