Purpose:Human activity recognition is essential for supporting independent living. Although image-based approaches have achieved significant progress, they raise privacy concerns, and require adequate and stable lighting conditions. Millimetre-wave (mmWave) radar provides a privacy-preserving alternative; however, its point cloud data are typically sparse, irregular, and noisy. Graph neural network–based methods, particularly those built on EdgeConv, aim to address the challenge of irregularity by modelling the relationships between points and their local neighbours. Conventional EdgeConv operators rely on a fixed set of \((k)\) nearest neighbours, using all neighbours deterministically during feature aggregation. Combined with dense feature transformations, this design has a high computational cost and may reduce robustness, as redundant or noisy neighbours are always incorporated into the representation. Methods: To address these limitations, we propose SEdgeNet, a graph-based architecture for mmWave point-cloud activity recognition. The principal contribution of SEdgeNet is the introduction of Stochastic Edge Convolution (SEdgeConv), which comprises two components: Stochastic Neighbour Sampling (SNS) and Edge-wise Factorised Convolution (EFC). SNS processes only a subset of neighbouring points during each forward pass, while EFC is designed to model fine-grained interactions efficiently. SEdgeNet further incorporates multi-scale feature aggregation to enhance both local and global representations.  Results: Experiments on the MiliPoint and MMActivity datasets shows that SEdgeNet outperforms baseline methods in both accuracy and computational efficiency, achieving state-of-the-art performance.  Conclusion: These results highlight the effectiveness of SEdgeNet and promising potential of mmWave radar for privacy-preserving activity monitoring. The code is available at: \href{https://github.com/Gbouna/SEdgeNet}{https://github.com/Gbouna/SEdgeNet}.