The central issue in representing graph-structured data instances in learning algorithms is designing features which are invariant to permuting the numbering of the vertices. We present a new system of invariant graph features which we call the skew spectrum of graphs. The skew spectrum is based on mapping the adjacency matrix to a function on the symmetric group and computing bispectral invariants. The reduced form of the skew spectrum is computable in \m{O(n^3)} time, and experiments show that on several benchmark datasets it can outperform state of the art graph kernels.