Emergence of the giant weak component in directed random graphs with arbitrary degree distributions.

@article{Kryven2016EmergenceOT,
  title={Emergence of the giant weak component in directed random graphs with arbitrary degree distributions.},
  author={Ivan Kryven},
  journal={Physical review. E},
  year={2016},
  volume={94 1-1},
  pages={
          012315
        }
}
  • I. Kryven
  • Published 2016
  • Mathematics, Medicine
  • Physical review. E
The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for the existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In addition, we consider a random process for evolving directed graphs with bounded degrees. The bounds are not the same for different vertices but satisfy a predefined distribution. The analytic expression obtained for the evolving degree distribution is… Expand

Figures, Tables, and Topics from this paper

Connectivity of a general class of inhomogeneous random digraphs
TLDR
It is shown that by choosing the joint distribution of the vertex attributes according to a multivariate regularly varying distribution, one can obtain scale-free graphs with arbitrary in-degree/outdegree dependence. Expand
Algebraic bounds for heterogeneous site percolation on directed and undirected graphs
TLDR
It turns out to be the uniqueness criterion that is most closely associated with an asymptotically vanishing probability of forming a giant strongly-connected component on a large finite (di)graph. Expand
Networks with degree-degree correlations is a special case of edge-coloured random graphs
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary jointExpand
Networks with degree–degree correlations are special cases of the edge-coloured random graph
In complex networks, the degrees of adjacent nodes may often appear dependent—which presents a modelling challenge. We present a working framework for studying networks with an arbitrary jointExpand
Universality for the directed configuration model with random degrees: metric space convergence of the strongly connected components at criticality
We consider the strongly connected components (SCCs) of a uniform directed graph on n vertices with i.i.d. degree tuples distributed as (D−, D), with E[D] = E[D−] = μ. We condition on the totalExpand
Analytic results on the polymerisation random graph model
  • I. Kryven
  • 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 differentExpand
Linear stability analysis for large dynamical systems on directed random graphs.
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees.Expand
Dynamic Networks that Drive the Process of Irreversible Step-Growth Polymerization
TLDR
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
Bond percolation in coloured and multiplex networks
  • I. Kryven
  • Medicine, Physics
  • Nature Communications
  • 2019
TLDR
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
Coloured random graphs explain the structure and dynamics of cross-linked polymer networks
TLDR
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
...
1
2
3
...

References

SHOWING 1-10 OF 56 REFERENCES
MATH
Abstract: About a decade ago, biophysicists observed an approximately linear relationship between the combinatorial complexity of knotted DNA and the distance traveled in gel electrophoresisExpand
Advances in Knowledge Discovery and Data Mining
TLDR
This work shows how the nonlinear reconstruction of the underlying dynamical system by way of time delay embedding yields a new solution for denoising where the underlying dynamics is assumed to be highly non-linear yet low-dimensional. Expand
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)Expand
Macromol
  • Theor. Simul. 25, 348 (2016). 012315-10 EMERGENCE OF THE GIANT WEAK COMPONENT IN . . . PHYSICAL REVIEW E 94, 012315
  • 2016
Macromolecular Theory and Simulations 24
  • 248
  • 2015
Phys
  • Rev. E 64, 026118
  • 2001
Physical review E 64
  • 026118
  • 2001
Journal of Mathematical Physics 2
  • 609
  • 1961
Combinator
  • Probab. Comput. 7, 295
  • 1998
Random Struct
  • Algorithms 6, 161
  • 1995
...
1
2
3
4
5
...