## 1 Introduction
This framework effectively reduces the handover failure rates and avoids unnecessary handovers. [PERSON] et al. [28] proposed a graph-based customizable handover framework that considers both the handover time and the target in selecting a sequence, ensuring QoS. By finding shortest paths in a time-based graph, the framework determines the optimal handover sequence and time to meet desired QoS. [PERSON] et al. [29] proposed an intelligent handover strategy employing a multi-attribute graph (MAG) and a genetic algorithm to optimize the handover process, consequently reducing communication delay and handover time. Currently, the integration of traditional handover algorithms with machine learning algorithms has become a prominent research area. [PERSON] proposed a Deep Q-Network (DQN) model to optimize the handover process of LEO satellites in non-terrestrial networks (NTNs). This model considers various handover criteria and demonstrates convergence. [PERSON] et al. [30] proposed a satellite handover strategy based on deep reinforcement learning (DRL), reducing satellite handover time by simultaneously considering multiple factors. [PERSON] et al. [31] proposed a convolutional neural network-based handover strategy. Here, users can make near-optimal handover decisions based on historical signal strength, extracted using a convolutional neural network to reveal potential optimal handover strategies. Existing research generally falls into two categories: the handover algorithm considers relatively individual factors, which overlooks the impact of other handover factors, resulting in a higher handover failure rate; or focuses solely on selecting the next moment handover satellite, leading to local optima, which may not be the optimal choice for the entire communication duration, resulting in unnecessary handovers [32]. Regarding this, this paper proposes a satellite handover optimization algorithm, termed MPNN-DQN, based on the combination of graph neural networks and reinforcement learning, building upon the satellite handover framework grounded in graph theory. This algorithm comprehensively considers multiple attributes, including the remaining service time, propagation delay, and user data rate, with the objective of maximizing the quality of service. This approach enables the handover algorithm to make optimal decisions throughout the entire communication duration, minimizing the number of switches while satisfying user demand. The main contributions of the paper can be summarized as follows. In this paper, we first construct the satellite handover directed graph using graph theory, considering the remaining service time of the satellite and the potential handover between grid users and the satellite. Secondly, to maximize the service quality for power users, we propose a handover strategy that comprehensively weighs the service quality. This strategy assigns edge weights to the satellite handover directed graph based on three factors: the remaining service time, propagation delay, and user data rate. Next, within the graph-based LEO satellite handover framework, the processing capability of graph neural networks can enhance adaptability to changes in the satellite handover directed graph's topology. Learning the satellite handover graph structure and edge weight information enables us to obtain the satellite network state representation. The satellite handover algorithm, employing the DQN algorithm, models and analyzes the handover process throughout the communication duration, with grid users' service quality serving as a reward function to determine the optimal path in the satellite handover directed graph. Finally, experimental simulations are conducted to validate the effectiveness of the proposed algorithm.