EUGENE: Explainable Unsupervised Approximation of Graph Edit Distance with Generalized Edit Costs

Abstract: The need to identify graphs with small structural distances from a query arises in various domains such as biology, chemistry, recommender systems, and social network analysis. Among several methods for measuring inter-graph distance, Graph Edit Distance (GED) is preferred for its comprehensibility, though its computation is hindered by NP-hardness. Unsupervised methods often face challenges in providing accurate approximations. State-of-the-art GED approximations predominantly utilize neural methods, which, however, have several limitations: (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 EUGENE, an efficient algebraic unsupervised method that approximates GED while providing edit paths corresponding to the approximated cost. Extensive experimental evaluation demonstrates that EUGENE achieves state-of-the-art performance in GED estimation and exhibits superior scalability across diverse datasets and generalized cost settings.