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

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I. Kryven

Combinatorics · Submitted 13 Sep 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim If first partial moments of the degree distribution are finite, the size distribution for two-layer connected components in multiplex networks exhibits exponent $-\frac{3}{2}$ in the critical regime, whereas the size distribution of weakly connected components in directed networks exhibits two critical exponents, $-\frac{1}{2}$ and $-\frac{3}{2}$.

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arXiv ID1709.04283 (version 2)
Pith ID5QESOX2V, Pith's permanent record of this paper and its review
CitationI. Kryven. "Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions." arXiv:1709.04283 (2017). https://pith.science/paper/5QESOX2V
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,066 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.80 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with 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 exponent $-\frac{3}{2}$ in the critical regime, whereas the size distribution of weakly connected components in directed networks exhibits two critical exponents, $-\frac{1}{2}$ and $-\frac{3}{2}$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with arbitrary number of layers. contribution 1.00 0.95 0.38 asserted 1.00
s1 The expressions are computable in a polynomial time, and, under some restrictions, are tractable from the asymptotic theory point of view. method 0.36 0.82 0.07 asserted 0.96
s2 If first partial moments of the degree distribution are finite, the size distribution for two-layer connected components in multiplex networks exhibits exponent $-\frac{3}{2}$ in the critical regime, whereas the size distribution of weakly connected components in directed networks exhibits two critical exponents, $-\frac{1}{2}$ and $-\frac{3}{2}$. result 1.00 0.89 0.64 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with 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 exponent $-\frac{3}{2}$ in the critical regime, whereas the size distribution of weakly connected components in directed networks exhibits two critical exponents, $-\frac{1}{2}$ and $-\frac{3}{2}$.

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