General expression for component-size distribution in infinite configuration networks

@article{Kryven2017GeneralEF,
  title={General expression for component-size distribution in infinite configuration networks},
  author={Ivan Kryven},
  journal={Physical review. E},
  year={2017},
  volume={95 5-1},
  pages={
          052303
        }
}
  • I. Kryven
  • Published 2017
  • Mathematics, Medicine, Computer Science
  • Physical review. E
In the infinite configuration network the links between nodes are assigned randomly with the only restriction that the degree distribution has to match a predefined function. This work presents a simple equation that gives for an arbitrary degree distribution the corresponding size distribution of connected components. This equation is suitable for fast and stable numerical computations up to the machine precision. The analytical analysis reveals that the asymptote of the component size… Expand
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References

SHOWING 1-10 OF 71 REFERENCES
Networks: An Introduction
TLDR
This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Expand
Combinatorial species and tree-like structures
The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for theExpand
Applied Mathematics and Computation
TLDR
The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions by introducing graphs representing the domain of integration of the integrals in each term. Expand
Chance and Stability, Stable Distributions and Their Applications
Part 1 Theory: probability elementary introduction to the theory of stable laws characteristic functions probability densities integral transformations special functions and equations multivariateExpand
Communications in Statistics-Theory and Methods
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and ourExpand
Structure Discovery in Natural Language
  • Chris Biemann
  • Computer Science
  • Theory and Applications of Natural Language Processing
  • 2012
TLDR
This book sets an ambitious goal: to shift the development of language processing systems to a much more automated setting than previous works, and describes several procedures that let the computer discover structures without supervision in order to boost the performance of language technology applications. Expand
APPL
Statistical packages have been used for decades to analyze large datasets or to perform mathematically intractable statistical methods. These packages are not capable of working with random variablesExpand
Chemical Engineering Scienceについて
First Year – Fall ......................... .............................................................................................. Credits MAT 210 .....................................Expand
Phys
  • Rev. E 64, 026118
  • 2001
Physical review E 64
  • 026118
  • 2001
...
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4
5
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