# GraphSAGE-Based Multi-Path Reliable Routing Algorithm for Wireless Mesh Networks
## 1 Introduction
), and it is difficult to extend the trained models to different network topologies [12]. Graph neural network (GNN) is a new neural network structure that can effectively extract irregular topological information [13]. The model of GNN represents the node features in the network vectorially and updates iteratively according to the network topological relation. The authors of [14] propose the graph convolutional neural network (GCN) by adding convolutional operators to GNN, which can extract complex deep information in the graph structure and has a better representation ability for network topology and node features. Ref. [15] proposes GraphSAGE based on GCN. GraphSAGE is an inductive learning architecture that uses information from the current node and neighbor nodes to form feature vectors by aggregation. It can represent the feature vector of any node by aggregation function and has generalization ability while retaining the capability of good feature extraction of GCN. Therefore, GraphSAGE can be applied to routing algorithms in the face of complex node features and changing network environments in WMN. In response to the problems that traditional routing algorithms in WMN have low network resource utilization and are difficult to guarantee the reliability of transmission, this paper proposes a reliable routing algorithm that combines the improved breadth-first search and GraphSAGE. The algorithm consists of two parts, including a multi-path routing algorithm based on the improved breadth-first search and a GraphSAGE-based performance optimization algorithm. The main contributions of this paper are as follows:  
1. Propose a multi-path routing algorithm based on the improved breadth-first search. The algorithm can traverse the information of all neighbor nodes of the source, calculate the shortest hop count and predecessor nodes from neighbor nodes to the source, and then output all shortest paths based on this information. 2. Based on the multiple shortest paths found, a GraphSAGE-based performance optimization algorithm is proposed. The algorithm can generate network labels to train the GraphSAGE model. And then the network performance value of each node is obtained according to the inputting network topology, node features, and the trained GraphSAGE model. The network performance of each shortest path is composed of the sum of the network performance of each node in the path. Eventually, the path with the best network performance is selected for data transmission. 3. The proposed algorithm is evaluated from the effects of data sending rate, topology size, and channel environment on network performance (average end-to-end delay, packet loss rate, and throughput), respectively. The rest of the paper is organized as follows: Section 2 presents the system model. Section 3 presents the multi-path routing algorithm based on the improved breadth-first search. Section 4 presents the GraphSAGE-based performance optimization algorithm. The simulation methodology and results are shown in Section 5. Finally, Section 6 summarizes the findings of the paper.