Next Point-of-Interest (POI) recommendation plays a crucial role in urban mobility applications. Recently, POI recommendation models based on Graph Neural Networks (GNN) have been extensively studied and achieved, however, the effective incorporation of both spatial and temporal information into such GNN-based models remains challenging. Extracting distinct fine-grained features unique to each piece of information is difficult since temporal information often includes spatial information, as users tend to visit nearby POIs. To address the challenge, we propose \textbf{\underline{Mob}}ility \textbf{\underline{G}}raph \textbf{\underline{T}}ransformer (MobGT) that enables us to fully leverage graphs to capture both the spatial and temporal features in users' mobility patterns. MobGT combines individual spatial and temporal graph encoders to capture unique features and global user-location relations. Additionally, it incorporates a mobility encoder based on Graph Transformer to extract higher-order information between POIs. To address the long-tailed problem in spatial-temporal data, MobGT introduces a novel loss function, Tail Loss. Experimental results demonstrate that MobGT outperforms state-of-the-art models on various datasets and metrics, achieving 24\% improvement on average. Our codes are available at \url{https://github.com/Yukayo/MobGT}.
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