EUGENE: Explainable Unsupervised Approximation of Graph Edit Distance

The need to identify graphs having small structural distance from a query arises in biology, chemistry, recommender systems, and social network analysis. Among several methods to measure inter graph distance, Graph Edit Distance (GED) is preferred for its comprehensibility, yet hindered by the NP-hardness of its computation. State-of-the-art GED approximations predominantly employ neural methods, which, however, (i) lack an explanatory edit path corresponding to the approximated GED; (ii) require the NP-hard generation of ground-truth GEDs for training; and (iii) necessitate separate training on each dataset. In this paper, we propose an efficient algebraic unsuper vised method, EUGENE, that approximates GED and yields edit paths corresponding to the approx imated cost, while eliminating the need for ground truth generation and data-specific training. Extensive experimental evaluation demonstrates that the aforementioned benefits of EUGENE do not come at the cost of efficacy. Specifically, EUGENE consistently ranks among the most accurate methods across all of the benchmark datasets and outperforms majority of the neural approaches.