Degree Distribution of the FKP Network Model

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 a...

• Type: Conference
• Year: 2003
• Where: ICALP
• Authors: Noam Berger, Béla Bollobás, Christian Borgs, Jennifer T. Chayes, Oliver Riordan
• Keywords: Degree Sequence, ICALP 2003, Power Laws, Small Fraction, Theoretical Computer Science