Abstract: While graphs with continuous node attributes arise in many applications, state-of-the-art graph kernels for comparing continuous-attributed graphs suffer from a high runtime complexity; for instance, the popular shortest path kernel scales as $\mathcal{O}(n^4)$, where $n$ is the number of nodes. In this paper, we present a class of path kernels with computational complexity $\mathcal{O}(n^2 (m + \delta^2))$, where $\delta$ is the graph diameter and $m$ the number of edges. Due to the sparsity and small diameter of real-world graphs, these kernels scale comfortably to large graphs. In our experiments, the presented kernels outperform state-of-the-art kernels in terms of speed and accuracy on classification benchmark datasets.