Many of clustering algorithms are based on density estimates in R^d . Building geometric graphs on the dataset X is an elegant way of doing this. In fact, the connected components of a geometric graph match exactly with the high-density clusters of the 1-Nearest Neighbor density estimator. In this paper, We show that the natural way to generalize geometric graphs is to use hypergraphs with a more restrictive notion of connected component called K-Polyhedron. Herein, we prove that K-polyhedra correspond to high-density clusters of K-Nearest Neighbors density estimator. Furthermore, the percolation phenomenon is omnipresent behind the family of clustering algorithms we look at in this paper.