Being an indispensable component in location-based social networks, next point-of-interest (POI) recommendation recommends users unexplored POIs based on their recent visiting histories. However, existing work mainly models check-in data as isolated POI sequences, neglecting the crucial collaborative signals from cross-sequence check-in information. Furthermore, the sparse POI-POI transitions restrict the ability of a model to learn effective sequential patterns for recommendation. In this paper, we propose Sequence-to-Graph (Seq2Graph) augmentation for each POI sequence, allowing collaborative signals to be propagated from correlated POIs belonging to other sequences. We then devise a novel Sequence-to-Graph POI Recommender (SGRec), which jointly learns POI embeddings and infers a users temporal preferences from the graph-augmented POI sequence. To overcome the sparsity of POI-level interactions, we further infuse category-awareness into SGRec with a multi-task learning scheme that captures the denser category-wise transitions. As such, SGRec makes full use of the collaborative signals for learning expressive POI representations, and also comprehensively uncovers multi-level sequential patterns for user preference modelling. Extensive experiments on two real-world datasets demonstrate the superiority of SGRec against state-of-the-art methods in next POI recommendation.