General expression for the component size distribution in infinite configuration networks

Kryven, Ivan

doi:10.1103/physreve.95.052303

Cited by 27 publications

(34 citation statements)

References 34 publications

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“…[18] and, unlike in the case of directed networks, no new asymptotic modes emerge when the excess distribution is degenerate.…”

Section: Asymptotic Analysis For a Bilayer Networkmentioning

confidence: 86%

“…[18], one immediately obtains formal solutions in terms of the convolution power of the degree distribution,…”

Section: A Sizes Of In and Out Componentsmentioning

confidence: 99%

“…[18] for the derivation. One can see that, depending on the values of the moments, the asymptotes (18) and (19) switch between exponential and algebraic decays.…”

Section: Asymptotes For In and Out Componentsmentioning

confidence: 99%

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Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions

Kryven

2017

Phys. Rev. E

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Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions Kryven, I. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. This work presents exact expressions for size distributions of weak and multilayer connected components in two generalizations of the configuration model: networks with directed edges and multiplex networks with an arbitrary number of layers. The expressions are computable in a polynomial time and, under some restrictions, are tractable from the asymptotic theory point of view. If first partial moments of the degree distribution are finite, the size distribution for two-layer connected components in multiplex networks exhibits an exponent − 3 2 in the critical regime, whereas the size distribution of weakly connected components in directed networks exhibits two critical exponents − .

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“…[18] and, unlike in the case of directed networks, no new asymptotic modes emerge when the excess distribution is degenerate.…”

Section: Asymptotic Analysis For a Bilayer Networkmentioning

confidence: 86%

“…[18], one immediately obtains formal solutions in terms of the convolution power of the degree distribution,…”

Section: A Sizes Of In and Out Componentsmentioning

confidence: 99%

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Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions

Kryven

2017

Phys. Rev. E

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“…This approach is most accurately placed within the emerging field of "random graph modeling" that only recently started to diffuse into chemistry. [50][51][52][53][54] A random graph refers to a probability distribution over all possible realizations of a graph and allows us to draw results that are typical to MC simulations with an analytical probabilistic consideration. One of the most attractive features is that results on random graphs are often obtainable as an explicit exact equation bypassing any simulations at all.…”

Section: Introductionmentioning

confidence: 99%

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

Schamboeck

Kryven

Iedema

2017

Macro Theory & Simulations

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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 gel. The model is based on a new graph theoretical concept being introduced in the framework of population balance equations (PBEs) for monomer states (mPBEs). A trivariate degree distribution that describes the topology of the network locally is obtained from the mPBE, which serves as an input for a directional random graph model. Thus, access is granted to global properties of the acrylate network which include molecular size distribution, distributions of molecules with a specific number of crosslinks/radicals, gelation time/conversion, and gel/sol weight fraction. Furthermore, an analytic criterion for gelation is derived. This criterion connects weight fractions of converted monomers and the transition into the gel regime. Valid results in both sol and gel regimes are obtained by the new model, which is confirmed by a comparison with a “classical” macromolecular PBE model. The model predicts full transition of polymer into gel at very low vinyl conversion (<2%). Typically, this low‐conversion network is very sparse, as becomes apparent from the predicted crosslink distribution.

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“…As a result, studies to generate network models that resemble various kinds of real-world networks attract a lot of attention. Many methods were proposed to generate complex networks: rewiring model, growing model, configuration model, etc [6][7][8][9][10][11][12][13][14][15][16][17][18].The Watts-Strogatz (WS) model generates a smallworld network based on the rewiring method [6]. The small-world network has a high clustering coefficient and short average path length, but it has restriction in the degree distribution [6,7].The Barabási-Albert (BA) model generates a scale-free network using the growing model with the preferential attachment [8].…”

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confidence: 99%

Highly clustered complex networks in the configuration model: Random regular small-world network

Jeong¹,

Jang²,

Yu³

2019

EPL

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We propose a method to make a highly clustered complex network within the configuration model. Using this method, we generated highly clustered random regular networks and analyzed the properties of them. We show that highly clustered random regular networks with appropriate parameters satisfy all the conditions of the small-world network: connectedness, high clustering coefficient, and small-world effect. We also study how clustering affects the percolation threshold in random regular networks. In addition, the prisoner's dilemma game is studied and the effects of clustering and degree heterogeneity on the cooperation level are discussed.Introduction. -Recently, complex networks have played important roles in various fields [1][2][3][4][5]. There are, especially, a lot of researches on the various types of realworld network structures [1,4,5]. As a result, studies to generate network models that resemble various kinds of real-world networks attract a lot of attention. Many methods were proposed to generate complex networks: rewiring model, growing model, configuration model, etc [6][7][8][9][10][11][12][13][14][15][16][17][18].The Watts-Strogatz (WS) model generates a smallworld network based on the rewiring method [6]. The small-world network has a high clustering coefficient and short average path length, but it has restriction in the degree distribution [6,7].The Barabási-Albert (BA) model generates a scale-free network using the growing model with the preferential attachment [8]. It produces the power-law degree distribution, which is frequently observed in a real-world network such as citation networks, metabolic networks, and the Internet [19][20][21][22][23]. However, the network generated by the BA model has a vanishing clustering coefficient in contrast with real-world networks. To overcome this problem of the BA model, many researchers proposed modified BA models [9][10][11][12] that have a high clustering coefficient maintaining the power-law degree distribution.The configuration model is a method to make a random network for a given arbitrary degree sequence. This (a)

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General expression for the component size distribution in infinite configuration networks

Cited by 27 publications

References 34 publications

Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions

Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions

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

Highly clustered complex networks in the configuration model: Random regular small-world network

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