  Let M be a bounded domain of a Euclidian space with smooth boundary. We
relate the Cheeger constant of M and the conductance of a neighborhood graph
defined on a random sample from M. By restricting the minimization defining the
latter over a particular class of subsets, we obtain consistency (after
normalization) as the sample size increases, and show that any minimizing
sequence of subsets has a subsequence converging to a Cheeger set of M.
