Learning Graph Matching with Graph Neural Networks

Graph matching aims at evaluating the dissimilarity of two graphs by defining a constrained correspondence between their nodes and edges. Error-tolerant graph matching, for instance, introduces the concept of a cost for penalizing structural differences in the matching. A popular method for this approach is graph edit distance, which is based on the cost of the minimal sequence of edit operations to transform a source graph into a target graph. One of the main problems of graph edit distance is the computational complexity, which is exponential in its exact form. In recent years, several approximation methods for graph edit distance have been presented which offer polynomial runtimes. In this paper, we approach the graph edit distance problem in a fundamentally different way. In particular, we propose to learn graph edit distance by means of graph neural networks. In a comprehensive experimental evaluation on six data sets, we verify that our approach not only provides comparable classification performance but also substantially reduces the runtime compared to a prominent algorithm for approximate graph edit distance computation.