Scale-free networks as pre-asymptotic regimes of super-linear preferential attachment

@article{Krapivsky2008ScalefreeNA,
  title={Scale-free networks as pre-asymptotic regimes of super-linear preferential attachment},
  author={Paul L. Krapivsky and Dmitri V. Krioukov},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2008},
  volume={78 2 Pt 2},
  pages={
          026114
        }
}
  • P. Krapivsky, Dmitri V. Krioukov
  • Published 2008
  • Mathematics, Medicine, Physics, Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing network models that perfectly match the structure of some real scale-free networks, such as the Internet. We obtain an analytic solution, supported by extensive simulations, for the degree distribution in superlinearly growing networks with arbitrary average… Expand
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References

SHOWING 1-10 OF 76 REFERENCES
Connectivity Transitions in Networks with Super-Linear Preferential Attachment
We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the pth power ofExpand
Structural constraints in complex networks
We present a link rewiring mechanism to produce surrogates of a network where both the degree distribution and the rich-club connectivity are preserved. We consider three real networks, theExpand
Cut-offs and finite size effects in scale-free networks
Abstract.We analyze the degree distribution’s cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices N is ruled by the topological constraintsExpand
Organization of growing random networks.
  • P. Krapivsky, S. Redner
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
TLDR
The organizational development of growing random networks is investigated, and the combined age and degree distribution of nodes shows that old nodes typically have a large degree. Expand
On the emergence of highly variable distributions in the autonomous system topology
TLDR
This paper constructs a model incorporating exponential growth in the size of the Internet and in the number of ASes, and shows that it yields a size distribution exhibiting a power-law tail and instantiates such a model with empirically derived estimates of historical growth rates and the resulting degree distribution is in good agreement with that of real AS graphs. Expand
Self-similarity of complex networks and hidden metric spaces
TLDR
These findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization. Expand
Emergence of scaling in random networks
TLDR
A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems. Expand
Finiteness and fluctuations in growing networks
We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks byExpand
Accurately modeling the Internet topology
  • Shi Zhou, R. Mondragón
  • Computer Science, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
TLDR
The positive-feedback preference (PFP) model is introduced which accurately reproduces many topological properties of the AS-level internet, including degree distribution, rich-club connectivity, the maximum degree, shortest path length, short cycles, disassortative mixing, and betweenness centrality. Expand
Connectivity of growing random networks.
TLDR
A solution for the time- and age-dependent connectivity distribution of a growing random network is presented and the power law N(k) approximately k(-nu) is found, where the exponent nu can be tuned to any value in the range 2. Expand
...
1
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3
4
5
...