*3.1. System Overview*

An illustration of the proposed framework **SORAG** is shown in Figure 3. **SORAG** is composed of four components: (1) the first part is in charge of determining the global minority degree (GMD) and local minority degree (LMD) of each node and constructing training data (i.e., seed examples) for the virtual node generator; (2) the second part, the node generator, is an ensemble of a GAN [25] network and a CGAN [27] network, where the GAN is responsible for creating unlabeled nodes and the CGAN is used for generating labeled nodes; (3) the third component is an edge generator. Its job is to create virtual edges between the synthetic and real nodes so that the generated nodes can participate in the message passing on the graph more effectively; (4) finally, a GCN-based node classifier is designed for learning the node representations of the augmented graph as well as the inter-label dependencies for multi-label node classification. We elaborate on each component as follows.

**Figure 3.** Overview of the **SORAG** framework. First, based on the feature matrix and the adjacency matrix of the input graph, we calculate the local minority degree (LMD) value of each node in the training set and classify it into one of the four types: safe (SF), borderline (BD), rare (RR), and outlier (OT). After that, we calculate the seed probability (SP) values of nodes in the SF and BD classes and select the seed nodes based on such values (see Section 3.2). Then, we use the seed nodes to train the node generator (i.e., the ensemble of GAN and CGAN) to generate high-quality unlabeled synthetic nodes and labeled synthetic nodes. Notice that by adjusting the objective function, we can flexibly manipulate the data distribution simulated by the node generator (see Section 3.3). With virtual nodes, an edge generator, which is essentially a feed-forward neural network, is used to generate virtual edges connecting the virtual nodes and the real nodes. The role of the generated edges is to facilitate feature propagation between two types of nodes (see Section 3.4). Finally, the new graph containing virtual nodes and virtual edges is fed into a GCN that learns the discriminative graph embeddings and performs effective node classification. During this process, the label correlation matrix provides helpful label correlation and interaction information (see Section 3.5).
