Graph Neural Networks (GNNs) have garnered intensive attention for Network Intrusion Detection System (NIDS) due to their suitability for representing the network traffic flows. However, most present GNN-based methods for NIDS are supervised or semi-supervised. Network flows need to be manually annotated as supervisory labels, a process that is time-consuming or even impossible, making NIDS difficult to adapt to potentially complex attacks, especially in large-scale real-world scenarios. The existing GNN-based self-supervised methods focus on the binary classification of network flow as benign or not, and thus fail to reveal the types of attack in practice. This paper studies the application of GNNs to identify the specific types of network flows in an unsupervised manner. We first design an encoder to obtain graph embedding, that introduces the graph attention mechanism and considers the edge information as the only essential factor. Then, a self-supervised method based on graph contrastive learning is proposed. The method samples center nodes, and for each center node, generates subgraph by it and its direct neighbor nodes, and corresponding contrastive subgraph from the interpolated graph, and finally constructs positive and negative samples from subgraphs. Furthermore, a structured contrastive loss function based on edge features and graph local topology is introduced. To the best of our knowledge, it is the first GNN-based self-supervised method for the multiclass classification of network flows in NIDS. Detailed experiments conducted on four real-world databases (NF-Bot-IoT, NF-Bot-IoT-v2, NF-CSE-CIC-IDS2018, and NF-CSE-CIC-IDS2018-v2) systematically compare our model with the state-of-the-art supervised and self-supervised models, illustrating the considerable potential of our method. Our code is accessible through https://github.com/renj-xu/NEGSC.