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arXiv · 1709.04283

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

I. Kryven
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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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I. Kryven. 2017-10-20. Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions. https://doi.org/10.1103/physreve.96.052304

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