The paper introduces the Graph Kolmogorov–Arnold Network (GKAN), a novel graph neural network (GNN) model that leverages spline-based activation functions on edges to enhance both accuracy and interpretability. GKAN is inspired by the Kolmogorov–Arnold representation theorem, which states that a multivariate function can be expressed as a finite sum of compositions of univariate functions. This principle is extended to GNNs, enabling the model to capture complex relationships in graph-structured data while maintaining interpretability. GKAN's architecture consists of multiple layers, including KAN-based convolutional and linear layers. The convolutional layers propagate and aggregate messages between nodes using spline-based activation functions, while the linear layer performs a final transformation on the aggregated features. The use of splines allows for flexible nonlinear transformations and provides inherent interpretability, as the model's decision-making process can be directly understood through the learned spline functions. Experiments on five benchmark datasets (Cora, PubMed, CiteSeer, MUTAG, and PROTEINS) demonstrate that GKAN outperforms state-of-the-art GNN models in node classification, link prediction, and graph classification tasks. Additionally, GKAN's design inherently provides clear insights into the model's decision-making process, eliminating the need for post-hoc explainability techniques. This makes GKAN particularly valuable in domains where interpretability is crucial, such as biomedical and financial applications. The paper also discusses the limitations of GKAN, including increased memory usage due to the use of splines and the lack of edge features in the current implementation. Future work includes optimizing the framework, incorporating edge features, and exploring real-world applications. Overall, GKAN represents a significant advancement in the development of accurate and interpretable GNNs.The paper introduces the Graph Kolmogorov–Arnold Network (GKAN), a novel graph neural network (GNN) model that leverages spline-based activation functions on edges to enhance both accuracy and interpretability. GKAN is inspired by the Kolmogorov–Arnold representation theorem, which states that a multivariate function can be expressed as a finite sum of compositions of univariate functions. This principle is extended to GNNs, enabling the model to capture complex relationships in graph-structured data while maintaining interpretability. GKAN's architecture consists of multiple layers, including KAN-based convolutional and linear layers. The convolutional layers propagate and aggregate messages between nodes using spline-based activation functions, while the linear layer performs a final transformation on the aggregated features. The use of splines allows for flexible nonlinear transformations and provides inherent interpretability, as the model's decision-making process can be directly understood through the learned spline functions. Experiments on five benchmark datasets (Cora, PubMed, CiteSeer, MUTAG, and PROTEINS) demonstrate that GKAN outperforms state-of-the-art GNN models in node classification, link prediction, and graph classification tasks. Additionally, GKAN's design inherently provides clear insights into the model's decision-making process, eliminating the need for post-hoc explainability techniques. This makes GKAN particularly valuable in domains where interpretability is crucial, such as biomedical and financial applications. The paper also discusses the limitations of GKAN, including increased memory usage due to the use of splines and the lack of edge features in the current implementation. Future work includes optimizing the framework, incorporating edge features, and exploring real-world applications. Overall, GKAN represents a significant advancement in the development of accurate and interpretable GNNs.