Edge networking brings computation and data storage as close to the point of request as possible. Various intelligent devices are connected to the edge nodes where traffic packets flow. Traffic classification tasks are thought to be a keystone for network management; researchers can analyze packets captured to understand the traffic as it hits their network. However, the existing traffic classification framework needs to conduct a unified analysis, which leads to the huge bandwidth resources required in the process of transferring all captured packet files to train a global classifier. In this paper, a semisupervised graph neural network traffic classifier is proposed for cloud-edge architecture so that cloud servers and edge nodes could cooperate to perform the traffic classification tasks in order to deliver low latency and save bandwidth on the edge nodes. To preserve the structural information and interrelationships conveyed in packets within a session, we transform traffic sessions into graphs. We segment the frequently combined consecutive packets into granules, which are later transformed into the nodes in graphs. Edges could extract the adjacency of the granules in the sessions; the edge node side then selects the highly representative samples and sends them to the cloud server; the server side uses graph neural networks to perform semisupervised classification tasks on the selected training set. Our method has been trained and tested on several datasets, such as the VPN-nonVPN dataset, and the experimental results show good performance on accuracy, recall, and F-score.