We propose graph kernels based on subgraphmatchings, i.e.structure-preserving bijec-tions between subgraphs. While recently pro-posed kernels based on common subgraphs(Wale et al., 2008; Shervashidze et al., 2009)in general can not be applied to attributedgraphs, our approach allows to rate mappingsof subgraphs by a flexible scoring schemecomparing vertex and edge attributes by ker-nels. We show that subgraph matching ker-nels generalize several known kernels. Tocompute the kernel we propose a graph-theoretical algorithm inspired by a classicalrelation between common subgraphs of twographs and cliques in their product graph ob-served by Levi (1973). Encouraging experi-mental results on a classification task of real-world graphs are presented.

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