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By Riesen K., Bunke H.

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The definition of adequate and application-specific cost functions is a key task in edit distance based graph matching. e. the meaning of the graphs, prior knowledge of the graphs’ labels is often inevitable for graph edit distance to be a suitable proximity measure. This fact is often considered as one of the major drawbacks of graph edit distance. Contrariwise, the possibility to parametrize graph edit distance by means of a cost function crucially amounts for the versatility of this particular dissimilarity model.

These kernels measure the similarity of two graphs by the number of random walks in both graphs that have all or some labels in common [44, 45, 140, 145–147]. In [140] it is shown that the number of matching walks in two graphs can be computed by means of the product graph of two graphs, without the need to explicitly enumerate the walks. In order to handle continuous labels the random walk kernel has been extended in [44]. This extension allows one to also take non-identically labeled walks into account.

Error-tolerant graph matching methods, on the other hand, offer a framework for structural matching that reflects the intuitive understanding of graph similarity in a much broader sense. In general, the error-tolerant nature of such algorithms allows the mapping between substructures of two graphs even if the corresponding structures and labelings are not completely identical. In other words, differences on the labels of two nodes or edges to be matched are accepted and rather penalized than merely forbidden.

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