Edge detection is a fundamental task in computer vision, crucial for object recognition, segmentation, and scene understanding. Traditional methods often fail to capture complex edge structures due to their inability to model intricate relationships between pixels. Graph Neural Networks (GNNs), particularly Graph Attention Networks (GATs), have shown promise in addressing these limitations by leveraging graph structures to model pixel relationships. This paper explores the applicability of Graph Attention Networks in edge detection, highlighting their advantages over ordinary Graph convolutional Networks (GCNs) through rigorous mathematical reasoning. We integrate GATs into an edge detection framework based on an encoder-decoder structure with U-Net architecture and provide detailed theoretical and implementation insights. Furthermore, we discuss the hardware acceleration of GCNs and GATs with a reconfigurable dataflow architecture integrated in the Pytorch framework. The experimental results demonstrate the superior performance of GAT-based edge detection and the potential acceleration possible on reconfigurable edge platforms with limited resources. The key advantage of our proposed method is its hardware-friendly design, making it highly suitable for FPGA acceleration while also enabling efficient optimization through pruning of the network.