Homomorphism Count

Homomorphism counting, the task of determining the number of mappings between two graphs that preserve their structure, is a crucial problem in graph-based machine learning. Current research focuses on improving the expressive power of graph neural networks (GNNs) for this task, exploring novel architectures like generalized Weisfeiler-Leman algorithms and edge-centric message passing schemes to overcome limitations in counting complex subgraph patterns. These advancements aim to enhance the accuracy and interpretability of GNNs for various applications, including node and graph classification, by leveraging the rich structural information encoded in homomorphism counts. The development of efficient and expressive homomorphism counting methods holds significant promise for advancing the field of graph-based machine learning.