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Recipe recommendation systems play an essential role in helping people decide what to eat. Existing recipe recommendation systems typically focused on content-based or collaborative filtering approaches, ignoring the higher-order collaborative signal such as relational structure information among users, recipes and food items. In this paper, we formalize the problem of recipe recommendation with graphs to incorporate the collaborative signal into recipe recommendation through graph modeling. In particular, we first present URI-Graph, a new and large-scale user-recipe-ingredient graph. We then propose RecipeRec, a novel heterogeneous graph learning model for recipe recommendation. The proposed model can capture recipe content and collaborative signal through a heterogeneous graph neural network with hierarchical attention and an ingredient set transformer. We also introduce a graph contrastive augmentation strategy to extract informative graph knowledge in a self-supervised manner. Finally, we design a joint objective function of recommendation and contrastive learning to optimize the model. Extensive experiments demonstrate that RecipeRec outperforms state-of-the-art methods for recipe recommendation. Dataset and codes are available at https://github.com/meettyj/RecipeRec.