arXiv Machine Learning October 16, 2026 By Martin Carrasco, Olga Zaghen, Kavir Sumaraj, Erik Bekkers, Bastian Rieck

Graph Homomorphism Distortion: A structural (pseudo)-metric for attributed graphs

Read the original on arXiv Machine Learning →

The paper introduces a new (pseudo)-metric called graph homomorphism distortion, which quantifies how much node features must be distorted when mapping one attributed graph to another. This metric builds on metric geometry concepts and leverages graph homomorphisms to capture both structure and features. The authors show that the metric can be efficiently approximated, offers fine-grained graph distinction, and can serve as a structural encoding that enhances graph neural network predictions.

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