Percolation in random graphs with higher-order clustering

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