The advancement of AI technology has significantly influenced production activities, increasing the focus on copyright protection for AI models. Model perceptual hashing offers an efficient solution for retrieving the pirated models. Existing methods, such as handcrafted feature-based and dual-branch network-based perceptual hashing, have proven effective in detecting pirated models. However, these approaches often struggle to differentiate non-pirated models, leading to frequent false positives in model authentication and protection. To address this challenge, this paper proposes a structurally-aware perceptual model hashing technique that achieved reduced false positives while maintaining high true positive rates. Specifically, we introduce a method for converting the diverse neural network structures into graph structures suitable for DNN processing, then utilize a graph neural network to learn their structural features representation. Our approach integrates perceptual parameter-based model hashing, achieving robust performance with higher detection accuracy and fewer false positives. Experimental results show that the proposed method has only 3\% false positive rate when detecting the non-pirated model, and the detection accuracy of pirated model reaches more than 98\%.