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The problem of measuring similarity of graphs and their nodes is important ina range of practical problems. There is a number of proposed measures, some ofthem being based on iterative calculation of similarity between two graphs andthe principle that two nodes are as similar as their neighbors are. In ourwork, we propose one novel method of that sort, with a refined concept ofsimilarity of two nodes that involves matching of their neighbors. We proveconvergence of the proposed method and show that it has some additionaldesirable properties that, to our knowledge, the existing methods lack. Weillustrate the method on two specific problems and empirically compare it toother methods.

Measuring Similarity of Graphs and their Nodes by Neighbor Matching