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]. © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Berger, N., Bollobás, B., Borgs, C., Chayes, J., & Riordan, O. (2003). Degree distribution of the FKP network model. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2719, 725–738. https://doi.org/10.1007/3-540-45061-0_57
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