This paper introduces GraFPrint, an audio identification framework that leverages the structural learning capabilities of Graph Neural Networks (GNNs) to create robust audio fingerprints. Our method constructs a k-nearest neighbor (k-NN) graph from time-frequency representations and applies max-relative graph convolutions to encode local and global information. The network is trained using a self-supervised contrastive approach, which enhances resilience to ambient distortions by optimizing feature representation. GraFPrint demonstrates superior performance on large-scale datasets at various levels of granularity, proving to be both lightweight and scalable, making it suitable for real-world applications with extensive reference databases.