## 4 Methodology  
In the field of graph learning, designing the deep structure is always difficult. As is shown in Figure 6, CARE-GNN with single-layer architecture performs the best and suffers from the performance degradation as the number of layers increases. Based on CARE-GNN, we employ the layered graph neural network [7] architecture and residual structure [5] to make the following improvements. First, we utilize layered architecture in Figure 7 to expend the original model to deep structure. The input to the model is a batch of central nodes and the original dataset. Each layer is an independent GNN, of which the input includes the original dataset and the node embeddings calculated by previous layer. The model is trained layer by layer, and each layer will correct mistakes made by previous layers. Intuitively, it indicates that each layer of GNN can focus on solving a simpler sub-problem. Moreover, the sub-problem is caused by the invalid or incorrect feature extracted by previous layers. Therefore, the layer-by-layer progressive learning process means the model is less reliant on a certain layer than the single-layer model, which allows every layer to make mistakes to some extent. Moreover, the mistakes will soon be continuously corrected by subsequent layers. Moreover, the fact that each layer inherits the results calculated by previous layer and its input includes the original graph enables each layer to make better choices on sampling neighbors. In other words, each layer is able to select a different and better set of neighbors based on the results calculated by previous layers. As a result, more nodes can be taken into account, and the neighborhood can be expended. The nodes' information will be richer and more accurate with the layer-by-layer training. As the depth increases, the model is able to \"think\" for more times, and each time the model can \"think\" more deeply and comprehensively based on the achievements of previous layer, thereby making better inferences. We also take advantage of residual structure [5] to help the training process. The research points out that when adding multiple nonlinear layers to a shallow model, if the added layers can learn an identity mapping, which means the output equals to the input, then the performance of the model will at least not deteriorate. However, the fact is that it is  
Figure 6: Recall of CARE-GNN with different number of layers. difficult for the complicated neural networks to fit a potential identity mapping. To reduce the learning difficulty for the networks, we let the model optimize the residual mapping instead of the original mapping. The added networks will learn a function \(\mathcal{F}(G,\{W_{i}\})\) to fit a target mapping \(\mathcal{H}(G)\), where \(G\) and \(\{W_{i}\}\) are the input graph and a set of learnable parameters, respectively. As it is difficult for the networks to fit the identity mapping \(\mathcal{H}(G)=G\), we turn it to fit its residual function \(\mathcal{H}(G)-G\). Now, the function to be learned is \(\mathcal{F}(G,\{W_{i}\})=\mathcal{H}(G)-G\), and the target mapping is \(\mathcal{F}(G,\{W_{i}\})+G\). Therefore, the added nonlinear layers with residual structure still fits the desired underlying mapping. According to the form of the target mapping, we lead out a shortcut connection from input directly to the output. The work in [16] shows that adding shortcut connection for every GNN layer reaches the best result (see Figure 8). Combining the layered structure and residual structure, we show details of a single layer of RLC-GNN in Figure 9. For each layer, the input of similarity measure module consists of two parts. One is the original dataset, and another one is updated node embeddings from previous layer except the first layer. More precisely, at the first layer, the similarity measure module will directly use a batch of dataset and its neighbors' node embeddings from dataset to do the measurement. After the first layer, the input is the node embeddings calculated by previous layer (i.e., output of previous layer).