Mean-field theory for scale-free random networks

@article{Barabasi1999MeanfieldTF,
  title={Mean-field theory for scale-free random networks},
  author={A. L. Barabasi and R{\'e}ka Albert and Hawoong Jeong},
  journal={Physica A-statistical Mechanics and Its Applications},
  year={1999},
  volume={272},
  pages={173-187}
}
Scale-free networks from self-organization.
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  • 2005
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It is shown how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment, and the random walk algorithm is generalized to produce weighted networks with power-law distributions of both weight and degree.
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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.
Self-organized scale-free networks.
  • Kwangho Park, Y. Lai, N. Ye
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
TLDR
It is implied that it is natural for a complex network to self-organize itself into a scale-free state without growth, as in the first model, a spectrum of algebraic degree distributions with a small exponent can be generated.
Average path length in random networks.
TLDR
The result for 2<alpha<3 shows that structural properties of asymptotic scale-free networks including numerous examples of real-world systems are even more intriguing than ultra-small world behavior noticed in pure scale- free structures and for large system sizes N-->infinity there is a saturation effect for the average path length.
Weighted Scaling in Non-growth Random Networks
We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between
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A model of weighted scale-free networks incorporating a fit-gets-richer scheme which means the connectivity of the node depends on both the degree and fitness of the nodes, which indicates that asymptotically the scaling behaviors of the total weight distribution and the connectivity distribution are identical.
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A new growth model is introduced that allows to produce out-degree distributions that decay as a power-law with an exponent in the range from 1 to ∞.
Random Connection Based Scale-free Networks
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Through the simulation, this model absolutely has the characteristics of scale-free networks and the power-law distribution index is shown.
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