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An example of a kernel between graphs is the '''random walk kernel''',<ref name="Gaertner"/><ref name="Kashima"/> which conceptually performs [[random walk]]s on two graphs simultaneously, then counts the number of [[Path (graph theory)|path]]s that were produced by ''both'' walks. This is equivalent to doing random walks on the [[Tensor product of graphs|direct product]] of the pair of graphs, and from this, a kernel can be derived that can be efficiently computed.<ref name="Vishwanathan"/>
Another examples is the '''Weisfeiler-Leman graph kernel'''<ref>Shervashidze, Nino, et al. "Weisfeiler-lehman graph kernels." Journal of Machine Learning Research 12.9 (2011).</ref> which computes multiple rounds of the [[Weisfeiler-Leman algorithm]] and then computes the similarity of two graphs as the inner product of the histogram vectors of both graphs. In those histogram vectors the kernel collects the number of times a color occurs in the graph in every iteration.
Note that the Weisfeiler-Leman kernel in theory has an infinite dimension as the number of possible colors assigned by the Weisfeiler-Leman algorithm is infinite. By restricting to the colors that occur in both graphs, the computation is still feasible.
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