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 (4)

• Emergence of network features from multiplexity
• k-Core percolation on multiplex networks
• Component sizes in networks with arbitrary degree distributions
• Emergence of the giant weak-component in directed random graphs with arbitrary degree distributions

Cited by in corpus (2)

• Percolation on complex networks: Theory and application
• Networks with degree-degree correlations is a special case of edge-coloured random graphs