Weisfeiler Lehman

The Weisfeiler-Lehman (WL) test is a fundamental algorithm for assessing graph isomorphism, and its variants are crucial for understanding the expressive power of Graph Neural Networks (GNNs). Current research focuses on developing more nuanced metrics beyond the limitations of the standard WL test, including exploring concepts like homomorphism expressivity and graph biconnectivity to better quantify GNN capabilities. This work aims to improve GNN design and performance by providing a more precise understanding of their limitations and potential for improvement, impacting various applications relying on graph-structured data analysis. New algorithms like Twin-WL and modifications such as incorporating random walks and persistent homology are being explored to enhance GNN expressiveness and classification accuracy.