  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.
