In this paper, we develop a new entropic matching kernel for weighted graphs by aligning depth-based representations. We demonstrate that this kernel can be seen as an \textbf{aligned subtree kernel} that incorporates explicit subtree correspondences, and thus addresses the drawback of neglecting the relative locations between substructures that arises in the R-convolution kernels. Experiments on standard datasets demonstrate that our kernel can easily outperform state-of-the-art graph kernels in terms of classification accuracy.