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
Note on the heights of random recursive trees and random m‐ary search trees
Random Structures & Algorithms
Comparing Trade-off Based Models of the Internet
Fundamenta Informaticae
Comparing Trade-off Based Models of the Internet
Fundamenta Informaticae
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Power laws, in particular power-law degree distributions, have been observed in real-world networks in a very wide range of contexts, including social networks, biological networks, and artificial networks such as the physical internet or abstract world wide web. Recently, these observations have triggered much work attempting to explain the power laws in terms of new 'scale-free' random graph models. So far, perhaps the most effective mechanism for explaining power laws is the combination of growth and preferential attachment. In [A. Fabrikant, E. Koutsoupias, C.H. Papadimitriou, Heuristically optimized trade-offs: A new paradigm for power laws in the internet ICALP 2002, in: LNCS, vol. 2380, pp. 110-122], Fabrikant, Koutsoupias and Papadimitriou propose a new 'paradigm' for explaining power laws, based on trade-offs between competing objectives. They also introduce a new, simple and elegant parametrized model for the internet, and prove some kind of power-law bound on the degree sequence for a wide range of scalings of the trade-off parameter. Here we shall show that this model does not have the usual kind of power-law degree distribution observed in the real world: for the most interesting range of the parameter, neither the bulk of the nodes, nor the few highest degree nodes have degrees following a power law. We shall show that almost all nodes have degree 1, and that there is a strong bunching of degrees near the maximum.