Computing Graph Edit Distance via Neural Graph Matching

Graph edit distance (GED) computation is a fundamental NP-hard problem in graph theory. Given a graph pair ( G 1 , G 2 ), GED is defined as the minimum number of primitive operations converting G 1 to G 2 . Early studies focus on search-based inexact algorithms such as A*-beam search, and greedy algorithms using bipartite matching due to its NP-hardness. They can obtain a sub-optimal solution by constructing an edit path (the sequence of operations that converts G 1 to G 2 ). Recent studies convert the GED between a given graph pair ( G 1 , G 2 ) into a similarity score in the range (0, 1) by a well designed function. Then machine learning models (mostly based on graph neural networks) are applied to predict the similarity score. They achieve a much higher numerical precision than the sub-optimal solutions found by classical algorithms. However, a major limitation is that these machine learning models cannot generate an edit path. They treat the GED computation as a pure regression task to bypass its intrinsic complexity, but ignore the essential task of converting G 1 to G 2 . This severely limits the interpretability and usability of the solution.

In this paper, we propose a novel deep learning framework that solves the GED problem in a two-step manner: 1) The proposed graph neural network GEDGNN is in charge of predicting the GED value and a matching matrix; and 2) A post-processing algorithm based on k -best matching is used to derive k possible node matchings from the matching matrix generated by GEDGNN. The best matching will finally lead to a high-quality edit path. Extensive experiments are conducted on three real graph data sets and synthetic power-law graphs to demonstrate the effectiveness of our framework. Compared to the best result of existing GNN-based models, the mean absolute error (MAE) on GED value prediction decreases by 4.9% 74.3%. Compared to the state-of-the-art searching algorithm Noah, the MAE on GED value based on edit path reduces by 53.6% 88.1%.