With the increasing popularity of recommendation techniques and social networks, social network recommendation has become a significant research field, i.e., predicting a user's preferences based on her or his historical interaction data, because the social relationships of users can not only enrich their interaction information, but also imply the accurate characterization of their preferences. Although there are some existing studies that predict users' preferences by using the characteristics of social relationships, their time complexity and hardware resource consumption are often very expensive, which limits the feasibility in large-scale real-world scenarios. To address these issues, in this paper, we propose a simple and effective K-core Graph Collaborative Filtering (KGCF) model to incorporate the user's social features into a recommendation framework. The user's interaction information is auto-encoded linearly by incorporating the social relationship graph into the user's interaction information and constructing a multi-layer graph filter. The linear autoencoder graph filter alleviates the highly sparse data problem and dramatically reduces the training time and hardware resource consumption. Experimental results on several real-world datasets show the superior effectiveness and spatiotemporal efficiency compared with the existing baselines, especially the training speed is significantly accelerated for large-scale datasets.