Encryption protects internet users’ data security and privacy but makes network traffic classification a much harder problem. Network traffic classification is essential for identifying and predicting user behaviour which is important for the overall task of network management. Deep learning methods used to tackle this problem have produced promising results. However, the conditions on which these experiments are carried out raise questions about their effectiveness when applied in the real world. We tackle this problem by modelling network traffic as graphs and applying deep learning for classification. We design a graph classifier based on higher order graph neural network with the aim of optimum generalisation. To demonstrate the robustness of our model, we cross validate it on the ISCXVPN and USTC-TFC datasets with varying input specifications. We use our model to demonstrate the impact of network data truncation on traffic classification and define benchmarks for input specifications. Our best results outperform the state-of-the-art in terms of generalisation strength. Our tool is available online (https://github.com/zuluokonkwo/Encrypted-Network-Traffic-Classification-with-Higher-Order-Graph-Neural-Network ).