This paper proposes a novel Graph Neural Network-based Dynamic Malware (GNNDM) detection system that models network traffic and system call sequences as time-evolving attributed graphs, enabling the capture of complex relational dependencies that scalar feature vectors cannot represent. The proposed architecture employs discrete graph spectral analysis, leveraging the eigen spectrum of the normalized graph Laplacian matrix to construct permutation-invariant node embeddings that characterize both local topological neighbourhoods and global network communication patterns. An edge attention mechanism weighted by temporal co-occurrence statistics and entropy-differential features enhances the model’s sensitivity to subtle behavioural deviations indicative of covert lateral movement and command-and-control (C2) communication. The GNN-DM model is trained on a hybrid dataset comprising NSL-KDD, CICIDS-2021, and a proprietary SDN traffic trace containing 42 malware families collected in a high-fidelity testbed. Experimental results demonstrate that GNN-DM achieves 98.4% detection accuracy, 97.9% F1-score, and a false positive rate of 0.9%, outperforming CNN-LSTM baseline by 4.2 percentage points and SVM-based classifiers by 6.7 percentage points.