## 1 Introduction
It automates the selection of appropriate routing paths for the efficient transmission of network traffic by learning the data flow patterns and laws in the network. In the intelligent routing algorithm based on deep learning, the model first needs to be trained with a large amount of data, which include the network topological information, traffic load conditions, congestion information to learn patterns and laws of the network. Then, the trained deep learning model is utilized to make routing decisions. Compared with traditional routing algorithms, intelligent routing algorithms based on deep learning are able to monitor network traffic in real time and improve the overall network performance [7]. However, when the network topology changes, it needs to readjust the training labels to output the correct paths, so the traditional deep learning scheme cannot guarantee the correctness of the output paths. Moreover, the traditional deep learning scheme is not scalable. Even though the model is trained with the readjusted input data when the input network topology changes, this may cause a high processing latency. As an important branch of machine learning, DRL [8; 9] differs from supervised and unsupervised learning and involves learning interactively with the environment. Unlike traditional reinforcement learning methods, DRL uses deep neural networks (DNNs) instead of tables and expresses policies with function approximations. In this way, DRL avoids the dimensionality problem that traditional tabular reinforcement learning faces when dealing with complex real-world problems. Although trained DRL agents can significantly improve the routing optimization problem, they cannot work effectively in unknown network topologies. By analyzing the structure of DRL agents, the reason for this phenomenon can be found. In the case of a classical DQN, the inputs and dimensions of the model are determined by the actual network size (e.g., the size of the network topology). After the training is finished, the dimensions of the model inputs and outputs are fixed. Therefore, when facing networks of different sizes, the model is likely to receive inputs with anomalous dimension sizes. Although we can change the input dimensions by cutting or padding, it will destroy the potential topological information in the matrix. In addition, computer networks are essentially graphs, and existing methods that use neural networks to process state matrices are unable to learn the information in graph structures, which limits the performance of DRL in new networks. In conclusion, although DRL performs well in routing optimization, it cannot perform relational reasoning or graph structure generalizations to operate effectively in new network environments. A GNN is a neural network structure that can effectively deal with irregular topological information [10; 11; 12]. The basic principle of a GNN is to express and infer the nodes' characteristics through their local information and the relationship between neighboring nodes. Each node has an initial feature vector, which can be updated and improved through information interactions and aggregation with neighboring nodes. A GNN can be used to obtain global graph characterization and prediction results through multiple rounds of information transfers and feature updates. A graph convolutional neural network (GCN) is better able to characterize network structures and features, which can automatically extract the hidden and complex information patterns in a graph using a graph convolution operator. However, the GCN's shortcoming is that it only acquires the hidden features of all of the nodes and does not have the ability to scale. The GraphSAGE [13] model is an inductive learning architecture that uses information from the current node and neighboring nodes to form feature vectors by aggregation. GraphSAGE is able to represent feature vectors for any node through an aggregation function so that it has the ability to generalize, which is different from direct push learning.