## 3 Methodology
This score is pretty impressive and demonstrates the model's strong capability to precisely categorize both VPN and non-VPN traffic associated with multiple applications with a high degree of recall and precision. Our Graph Neural Network (GNN) models performed exceptionally well despite being more complex and requiring considerable training and provided with an F1 score of 99.3% (c.f Figure 5). Figure 4: Accuracy score for CNN and GNN. Figure 5: F1 score for CNN and GNN. Demonstrating a nearly ideal balance of precision and recall with a great F1 score, GNN was able to discriminate between the various types of VPN and non-VPN traffic connected with various apps; the GNN model achieved better results in this situation than the CNN model as clear from the findings. This could be attributed to the GNN's central ability to evaluate and maintain complex relationships and dependencies which contributes to the production of higher classification results. Recall: Analyzing a model's recall allows one to assess its ability to properly identify positive classes within a dataset that is often referred to as its sensitivity or true positive rate. Recall is the term for this category of the performance metric. In the context of our inquiry, the model's recall was assessed as a barometer of its ability to correctly differentiate between non-VPN network traffic and VPN network traffic. The recall score for our Convolutional Neural Network (CNN) models was calculated as 95.7%. According to this finding, CNN models were able to accurately classify 96% of non-VPN and VPN traffic related to different applications.In other words, the CNN models were highly efficient in detecting the true positive cases and only missed 4% of the positive classes. The Graph Neural Network (GNN) models also demonstrated a high recall score which is 99.6% (c.f Figure 6). With its inherent ability to handle complex relationships and dependencies inherent in network traffic, the GNN models were able to efficiently differentiate the diverse classes of VPN and non-VPN traffic linked with various applications. Upon comparison of the recall scores, it is evident that the GNN models surpassed the performance of the CNN models. This suggests that GNN models are better suited for this classification task, providing superior detection rates for true positive cases of VPN and non-VPN traffic related to different applications. Precision: Machine learning models are also rated in terms of precision, highlighting their capacity to distinguish between occurrences that truly qualify as positive and those that do not, demonstrating their capacity to appropriately select the genuine positive examples from among all those the model labels as positive. As it applies to our research, precision describes the model's ability to distinguish VPN traffic from non-VPN traffic associated with a number of different types of applications accurately. Our Convolutional Neural Network (CNN) models demonstrated a precision score of 95.2%. This implies that among all the network traffic instances that the CNN models classified as VPN or non-VPN, 95.2% were indeed correctly classified. Therefore, our CNN models successfully minimized the number of false positives, hence confirming their high precision. Meanwhile, the Graph Neural Network (GNN) models showcased impressive precision in distinguishing between different classes of VPN and non-VPN traffic associated with various applications. The score for GNN was 99.2% (c.f Figure 7). As a result of their

Figure 6: F1 score for CNN and GNN. ability to capture complex patterns and relationships within a network, GNN models have been able to reduce false positives, thus resulting in increased precision in their prediction of patterns. A comparative analysis of the precision scores reveals that the GNN models outshined the CNN models in our context. The superior precision of the GNN models indicates their enhanced proficiency in accurately identifying VPN and non-VPN traffic types, minimizing the risk of misclassification.