Random graphs with arbitrary clustering and their applications

Abstract

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in random graphs with higher-order clustering, arXiv e-prints, p. arXiv:2006.06744, June 2020.], we developed analytical solutions to the percolation properties of random networks with homogeneous clustering (clusters whose nodes are degree-equivalent). In this paper, we extend this model to investigate networks that contain clusters whose nodes are not degree-equivalent, including multilayer networks. Through numerical examples we show how this method can be used to investigate the properties of random complex networks with arbitrary clustering, extending the applicability of the configuration model and generating function formulation.

arXiv comment11 pages, 10 figures

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• Random graphs with arbitrary degree distributions and their applications
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• Higher-order organization of complex networks
• Random graphs with clustering
• Properties of highly clustered networks
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• Degree correlations in graphs with clique clustering
• Effectiveness of Contact Tracing on Networks with Cliques
• An exact formula for percolation on higher-order cycles
• Belief propagation on networks with cliques and chordless cycles
• Symbiotic and antagonistic disease dynamics on networks using bond percolatio
• Observability transitions in clustered networks
• Generating functions for message-passing on weighted networks: directed bond percolation and SIR epidemics
• Higher-order shortest paths in hypergraphs
• An exact N-strain epidemic model using bond percolation
• Construction of simplicial complexes with prescribed degree-size sequences