  In this paper we examine the percolation properties of higher-order networks
that have non-trivial clustering and subgraph-based assortative mixing (the
tendency of vertices to connect to other vertices based on subgraph joint
degree). Our analytical method is based on generating functions. We also
propose a Monte Carlo graph generation algorithm to draw random networks from
the ensemble of graphs with fixed statistics. We use our model to understand
the effect that network microstructure has, through the arrangement of
clustering, on the global properties. Finally, we use an edge disjoint clique
cover to represent empirical networks using our formulation, finding the
resultant model offers a significant improvement over edge-based theory.
