Percolation in random graphs with higher-order clustering

Abstract

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between neighbours. In this paper we use the generating function formulation to examine clustered networks that contain simple cycles and cliques of any order. We use the natural generalisation to the Molloy-Reed criterion for these networks to describe their critical properties and derive an analytical description of the size of the giant component, providing solutions for Poisson and power-law networks. We find that networks comprising larger simple cycles behave increasingly more tree-like. Conversley, clustering comprised of larger cliques increasingly deviate from the tree-like solution, although the behaviour is strongly dependent on the degree-assortativity.

11 pages, 6 figures

References in corpus (19)

• Random graphs with arbitrary degree distributions and their applications
• The spread of epidemic disease on networks
• Higher-order organization of complex networks
• Spectral redemption: clustering sparse networks
• Random graphs with clustering
• Properties of highly clustered networks
• Localization and centrality in networks
• Percolation on sparse networks
• Random graphs containing arbitrary distributions of subgraphs
• Percolation and Epidemic Thresholds in Clustered Networks
• How clustering affects the bond percolation threshold in complex networks
• Message passing on networks with loops
• Higher-order clustering in networks
• Bond percolation on a class of clustered random networks
• Higher order clustering coefficients in Barabasi-Albert networks
• Propagation dynamics on networks featuring complex topologies
• Beyond the locally tree-like approximation for percolation on real networks
• Spectra of networks containing short loops
• General and exact approach to percolation on random graphs

Cited by in corpus (8)

• Random graphs with arbitrary clustering and their applications
• Two-pathogen model with competition on clustered networks
• Cooperative coinfection dynamics on clustered networks
• Degree correlations in graphs with clique clustering
• An exact formula for percolation on higher-order cycles
• Symbiotic and antagonistic disease dynamics on networks using bond percolatio
• Belief propagation on networks with cliques and chordless cycles
• Observability transitions in clustered networks