The paper introduces Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural network architecture that extends the principles of Kolmogorov-Arnold Networks (KAN) to graph-structured data. GKANs use learnable spline-based functions instead of fixed linear weights, allowing for more dynamic feature propagation across graph structures. Two architectures are proposed: Architecture 1 applies learnable functions after aggregation, and Architecture 2 applies them before aggregation. Empirical evaluations on the Cora dataset show that GKANs achieve higher accuracy in semi-supervised learning tasks compared to traditional Graph Convolutional Networks (GCNs). The study also examines the impact of parameters such as the number of hidden nodes, grid size, and spline degree on the performance of GKANs. The results suggest that GKANs open a new avenue in graph representation learning and could serve as a foundation for various graph deep learning schemes.The paper introduces Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural network architecture that extends the principles of Kolmogorov-Arnold Networks (KAN) to graph-structured data. GKANs use learnable spline-based functions instead of fixed linear weights, allowing for more dynamic feature propagation across graph structures. Two architectures are proposed: Architecture 1 applies learnable functions after aggregation, and Architecture 2 applies them before aggregation. Empirical evaluations on the Cora dataset show that GKANs achieve higher accuracy in semi-supervised learning tasks compared to traditional Graph Convolutional Networks (GCNs). The study also examines the impact of parameters such as the number of hidden nodes, grid size, and spline degree on the performance of GKANs. The results suggest that GKANs open a new avenue in graph representation learning and could serve as a foundation for various graph deep learning schemes.