Detecting machine-generated code is crucial for maintaining software security and quality. Traditional approaches often rely on stylistic or statistical features, which are increasingly circumvented by advanced code generation models. This paper introduces a novel approach leveraging Graph Neural Networks (GNNs) to capture the structural characteristics of code, representing it as a program dependency graph. We demonstrate that our GNN-based classifier outperforms both traditional and embedding based methods on benchmark datasets, achieving improved accuracy and robustness in identifying code produced by various generation techniques. This work highlights the potential of GNNs for a more structural understanding of code authorship.