This paper proposes KAN-Driven Graph Networks: Multi-Domain Randomization and Regularization (MDRR-KAN) to address the issues of over-smoothing, insufficient robustness, and overfitting in graph neural networks (GNNs). Firstly, a multi-neighborhood Bernoulli random data augmentation method is proposed, which dynamically masks node features while fusing multi-order neighborhood information to balance local and global representations; then, we replace traditional MLPs with KAN neural networks to adaptively model complex feature interactions by employing learnable B-spline basis functions; lastly, a dual regularization mechanism that effectively suppresses noise interference and optimizes neighborhood information propagation. Experimental results demonstrate that MDRR-KAN achieves superior classification accuracy compared to mainstream GNN models (e.g., GCN, GAT) across multiple datasets. Notably, it maintains stable performance during deep propagation and exhibits only a 7% accuracy drop under 20% label noise, significantly outperforming baseline models. Visualization and ablation studies further validate its enhanced discriminative power and component-wise contributions, offering new insights for theoretical optimization and applications of graph neural networks.