Random graphs with arbitrary clustering and their applications

The structure of many real networks is not locally tree-like and hence, typical network analysis fails to characterise their bond percolation properties. In a recent paper, we developed analytical solutions to the percolation properties of random networks with homogeneous clustering (clusters whose node sites are equivalent). In this paper, we extend this model to investigate networks that contain clusters with multiple node sites present, 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.