Measuring Similarity of Graphs and their Nodes by Neighbor Matching

The problem of measuring similarity of graphs and their nodes is important in a range of practical problems. There is a number of proposed measures, some of them being based on iterative calculation of similarity between two graphs and the principle that two nodes are as similar as their neighbors are. In our work, we propose one novel method of that sort, with a refined concept of similarity of two nodes that involves matching of their neighbors. We prove convergence of the proposed method and show that it has some additional desirable properties that, to our knowledge, the existing methods lack. We illustrate the method on two specific problems and empirically compare it to other methods.