  The present paper is devoted to clustering geometric graphs. While the
standard spectral clustering is often not effective for geometric graphs, we
present an effective generalization, which we call higher-order spectral
clustering. It resembles in concept the classical spectral clustering method
but uses for partitioning the eigenvector associated with a higher-order
eigenvalue. We establish the weak consistency of this algorithm for a wide
class of geometric graphs which we call Soft Geometric Block Model. A small
adjustment of the algorithm provides strong consistency. We also show that our
method is effective in numerical experiments even for graphs of modest size.
