On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The Diameter of a Scale-Free Random Graph
Combinatorica
Adversarial deletion in a scale free random graph process
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Degree Distribution of Competition-Induced Preferential Attachment Graphs
Combinatorics, Probability and Computing
The workshop on internet topology (wit) report
ACM SIGCOMM Computer Communication Review
Adversarial Deletion in a Scale-Free Random Graph Process
Combinatorics, Probability and Computing
Limit theory for the random on-line nearest-neighbor graph
Random Structures & Algorithms
Local/Global Phenomena in Geometrically Generated Graphs
Algorithms and Models for the Web-Graph
Improved duplication models for proteome network evolution
RECOMB'05 Proceedings of the 2005 joint annual satellite conference on Systems biology and regulatory genomics
Not all scale free networks are Born equal: the role of the seed graph in PPI network emulation
RECOMB'06 Proceedings of the joint 2006 satellite conference on Systems biology and computational proteomics
A geometric preferential attachment model of networks II
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Construction of scale-free networks with partial information
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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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].