# GraphSAGE-Based Multi-Path Reliable Routing Algorithm for Wireless Mesh Networks
## 1 Introduction  
With the emergence of diverse scenarios, such as smart cities, intelligent transportation, and intelligent healthcare, many applications have very strict requirements for network performance. Wireless mesh networks (WMN) will be widely used and become part of the main bearer network in the future, which are an effective way to solve the \"last mile\" access problem on the Internet of Things (IoT) and the key to next-generation wireless network technology [1]. However, as more and more devices need to access wireless networks and generate abundant traffic, the performance improvement of WMN is greatly challenged. The traditional routing protocols can no longer adapt to complex network environments, so it is especially critical to research and design new routing protocols to improve the performance of WMN [2]. Researchers have proposed a lot of routing protocols for WMN, such as AODV (Ad hoc On-Demand Distance Vector Routing), DSDV (Destination-Sequenced Distance-Vector Routing), and DSR (Dynamic Source Routing) [3], which generate a single path. These protocols not only lead to the underutilization of network resources but also degrade overall network performance due to the oversee of some links. In order to solve such problems, some multi-path routing protocols have been proposed. A multi-path routing protocol MSR has been proposed in [4], which introduces a multipath mechanism based on DSR, improving the network performance. A hybrid multi-path routing protocol HWMP has been proposed in [5]. HWMP protocol combines AODV and a tree-type routing structure,which can obtain multiple paths from the source to the destination, improving the network resource utilization and network performance. A multi-path routing protocol JODB has been proposed in [6]. The protocol establishes multiple paths between the source and destination simultaneously, calculates each path metric, and then selects an appropriate path for data transmission according to different service requirements, which reduces the delay. A joint multi-path discovery and rate allocation algorithm has been proposed in [7], which evaluates the available bandwidth of multiple paths considering interference and allocates traffic based on the available bandwidth, improving the transmission efficiency. However, these multi-path routing protocols typically make assumptions for specific application scenarios to simplify the mathematical model, which are difficult to implement in real networks. In addition, the link states are changing all the time, and traditional routing protocols cannot quickly sense the changing environment and generate reliable routes. In recent years, intelligent algorithms based on machine learning have been introduced into the research of routing algorithms. Intelligent algorithms are data-driven and have the advantages of accuracy, efficiency, and generality, which enable them to adapt to dynamically changing network environments and diverse performance optimization requirements [8]. The authors of [9] propose an intelligent routing algorithm based on convolutional neural networks, which can give intelligent paths based on online training of traffic patterns. The algorithm increases the average network throughput by approximately 40%. The overall bandwidth utilization is achieved by about 70% compared with existing mechanisms. Ref. [9] proposes a Q-learning-based data-aggregation-aware energy-efficient routing algorithm for wireless sensor networks (WSN), which reduces the amount of data and extends the lifetime of the WSN. Ref. [10] proposes a routing decision scheme based on deep reinforcement learning, which obtains lower maximum link utilization and end-to-end delay. Existing approaches [9; 10; 11] usually use traditional neural networks such as recurrent neural networks (RNN) and convolutional neural networks (CNN) as the training subject. These neural networks can only handle Euclidean structured data, which is unsuitable for dynamically changing network topologies (for example, node deletion/addition, etc.