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.