This paper proposes a graph convolutional matrix completion (GC-MC) framework for matrix completion in recommender systems. The approach treats matrix completion as a link prediction problem on a bipartite graph, where user-item interactions are represented as edges. The model uses a graph auto-encoder that employs differentiable message passing on the bipartite interaction graph to learn latent user and item representations. These representations are then used in a bilinear decoder to reconstruct the rating matrix. The model outperforms recent state-of-the-art methods, especially when additional structured information such as social networks is available. The GC-MC model is trained using a combination of mini-batch and full-batch training, with a focus on efficient computation and regularization techniques. The model is evaluated on several benchmark datasets, including MovieLens, Flixster, Douban, and YahooMusic, demonstrating competitive performance. The paper also discusses related work, including auto-encoders, factorization models, and matrix completion with side information. The results show that the GC-MC model achieves state-of-the-art performance on these datasets, particularly in scenarios with limited user-item interactions. The model is also effective in cold-start scenarios, where users have very few ratings. The paper concludes that the GC-MC model is a promising approach for matrix completion in recommender systems, with potential for extension to multi-modal data and large-scale applications.This paper proposes a graph convolutional matrix completion (GC-MC) framework for matrix completion in recommender systems. The approach treats matrix completion as a link prediction problem on a bipartite graph, where user-item interactions are represented as edges. The model uses a graph auto-encoder that employs differentiable message passing on the bipartite interaction graph to learn latent user and item representations. These representations are then used in a bilinear decoder to reconstruct the rating matrix. The model outperforms recent state-of-the-art methods, especially when additional structured information such as social networks is available. The GC-MC model is trained using a combination of mini-batch and full-batch training, with a focus on efficient computation and regularization techniques. The model is evaluated on several benchmark datasets, including MovieLens, Flixster, Douban, and YahooMusic, demonstrating competitive performance. The paper also discusses related work, including auto-encoders, factorization models, and matrix completion with side information. The results show that the GC-MC model achieves state-of-the-art performance on these datasets, particularly in scenarios with limited user-item interactions. The model is also effective in cold-start scenarios, where users have very few ratings. The paper concludes that the GC-MC model is a promising approach for matrix completion in recommender systems, with potential for extension to multi-modal data and large-scale applications.