# 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 } }

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

#### Figures, Tables, and Topics from this paper

#### 16 Citations

Analytic results on the polymerisation random graph model

- Mathematics
- Journal of Mathematical Chemistry
- 2017

The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different… Expand

Statistical analysis of edges and bredges in configuration model networks.

- Mathematics, Medicine
- Physical review. E
- 2020

All the degree-degree correlations on the giant component are concentrated on the bredges, namely bredges tend to connect high degree nodes to low degree nodes and the implications are discussed in the context of common attack scenarios and network dismantling processes. Expand

Bond percolation in coloured and multiplex networks

- Medicine, Physics
- Nature Communications
- 2019

A generic analytic theory is established that describes how structure and sizes of all connected components in the network are affected by simple and colour-dependent bond percolations in coloured networks. Expand

Dynamic Networks that Drive the Process of Irreversible Step-Growth Polymerization

- Medicine, Physics
- Scientific Reports
- 2019

This paper proposes a generic model of step-growth polymerisation as a promising application of the percolation on a directed random graph, used to manufacture a broad range of polymeric materials, including: polyesters, polyurethanes, polyamides, and many others. Expand

Renormalization group for link percolation on planar hyperbolic manifolds.

- Medicine, Mathematics
- Physical review. E
- 2019

The role of network geometry in determining the nature of the percolation transition in planar hyperbolic manifolds is investigated and different universality classes can be observed depending on the value of the power-law exponent γ. Expand

Coloured random graphs explain the structure and dynamics of cross-linked polymer networks

- Computer Science, Medicine
- Scientific reports
- 2020

The theory quantifies and explains the gelation in free-radical polymerisation of cross-linked polymers and predicts conditions when history dependance has the most significant effect on the global properties of a polymer network. Expand

Automated reaction generation for polymer networks

- Computer Science
- Comput. Chem. Eng.
- 2018

A new modeling approach to complex polymerization is introduced that automatically constructs a reaction network, solves kinetic model, and retrieves such topological properties of the final polymer network as, for instance, distribution of molecular weight. Expand

Emergent patterns in complex networks

- Geography
- 2017

Complex interacting systems permeate the modern world. Many diverse natural, social and human made systems—ranging from food webs to human contact networks, to the Internet—can be studied in the… Expand

Acrylate Network Formation by Free-Radical Polymerization Modeled Using Random Graphs

- Materials Science
- 2017

A novel technique is developed to predict the evolving topology of a diacrylate polymer network under photocuring conditions, covering the low-viscous initial state to full transition into polymer… Expand

A Deterministic Model for Positional Gradients in Copolymers

- Materials Science
- 2018

Abstract A deterministic modelling approach is developed to predict the internal structure of gradient copolymer chains. A key innovation of the modelling approach is the introduction of a positional… Expand

#### References

SHOWING 1-10 OF 71 REFERENCES

Networks: An Introduction

- Computer Science
- 2010

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

- Mathematics, Computer Science
- Encyclopedia of mathematics and its applications
- 1997

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 the… Expand

Applied Mathematics and Computation

- Computer Science
- 2010

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

- Mathematics
- 1999

Part 1 Theory: probability elementary introduction to the theory of stable laws characteristic functions probability densities integral transformations special functions and equations multivariate… Expand

Communications in Statistics-Theory and Methods

- 2013

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 our… Expand

Structure Discovery in Natural Language

- Computer Science
- Theory and Applications of Natural Language Processing
- 2012

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

- 2001

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 variables… Expand

Chemical Engineering Scienceについて

- Engineering
- 1962

First Year – Fall ......................... .............................................................................................. Credits MAT 210 .....................................… Expand

Phys

- Rev. E 64, 026118
- 2001

Physical review E 64

- 026118
- 2001