A fully automatic mesh segmentation scheme using heterogeneous graphs is presented. We introduce a spectral framework where local geometry affinities are coupled with surface patch affinities. A heterogeneous graph is constructed combining two distinct graphs: a weighted graph based on adjacency of patches of an initial over-segmentation, and the weighted dual mesh graph. The partitioning relies on processing each eigenvector of the heterogeneous graph Laplacian individually, taking into account the nodal set and nodal domain theory. Experiments on standard datasets show that the proposed unsupervised approach outperforms the state-of-the-art unsupervised methodologies and is comparable to the best supervised approaches.