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Graph Neural Network (GNN) based recommender systems have been attracting more and more attention in recent years due to their excellent performance in accuracy. Representing user-item interactions as a bipartite graph, a GNN model generates user and item representations by aggregating embeddings of their neighbors. However, such an aggregation procedure often accumulates information purely based on the graph structure, overlooking the redundancy of the aggregated neighbors and resulting in poor diversity of the recommended list. In this paper, we propose diversifying GNN-based recommender systems by directly improving the embedding generation procedure. Particularly, we utilize the following three modules: submodular neighbor selection to find a subset of diverse neighbors to aggregate for each GNN node, layer attention to assign attention weights for each layer, and loss reweighting to focus on the learning of items belonging to long-tail categories. Blending the three modules into GNN, we present DGRec(Diversified GNN-based Recommender System) for diversified recommendation. Experiments on real-world datasets demonstrate that the proposed method can achieve the best diversity while keeping the accuracy comparable to state-of-the-art GNN-based recommender systems.