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

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 $-\frac{3}{2}$.

References in corpus (18)

• Assortative mixing in networks
• Random graphs with arbitrary degree distributions and their applications
• Multilayer Networks
• Mathematical Formulation of Multi-Layer Networks
• Emergence of network features from multiplexity
• Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
• Growing multiplex networks
• The Anatomy of a Scientific Rumor
• Percolation in Multiplex Networks with Overlap
• Hidden geometric correlations in real multiplex networks
• k-Core percolation on multiplex networks
• Bond percolation on multiplex networks
• Component sizes in networks with arbitrary degree distributions
• Weak percolation on multiplex networks
• Mutually connected component of network of networks with replica nodes
• Emergence of the giant weak-component in directed random graphs with arbitrary degree distributions
• General expression for the component size distribution in infinite configuration networks
• Analytical results on the polymerisation random graph model

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• Networks with degree-degree correlations is a special case of edge-coloured random graphs