Many of clustering algorithms for a point cloud Xn ⊂ R d in the Euclidean space are based on density estimates. In fact, the density function f of point generation contains the relevant information. It is quite natural to try to extract what Hartigan called ‘high-density clusters’. One elegant solution to do this task consists in constructing a graph whose nodes are the points of the cloud and whose edges connect nearby points. We want the connected components of this graph to reflect the high-density clusters. Some very classical algorithms such as (Robust) SingleLinkage or (H)DBSCAN work in this way. It is particularly helpful because its connected components correspond exactly to the high-density clusters of the density estimator of the 1-Nearest Neighbor. An example of the Single-Linkage will show us the mathematical phenomenon at the heart of these algorithms: the percolation. We define and measure the percolation rate to evaluate the performance of such algorithms. By way of example, we look at the Robust Single-Linkage algorithm and calculate its percolation rate. This will show theoretically why it is actually preferable to use K-Nearest Neighbours rather than 1-NN. However, convergence in K towards a perfect estimator is very slow, so this analysis explains why in practice K = 10 is often a good trade-off.