<p>Clustering is an important field of study in data analysis, and semi-supervised clustering, as a sub-category of clustering, has received extensive attention for significantly improving performance with only a small amount of prior information introduced. In recent years, many studies have incorporated semi-supervision into their field. Although good results have been obtained, most of these methods, when introducing additional information (for example, multi-view information), could not make full use of the given knowledge to mine intra-class similarity, and achieved suboptimal performance. For this situation, we put forward a new method of Semi-supervised Graph Convolutional Deep Embedding Clustering (SGDEC), which is a single-view algorithm. Specifically, an autoencoder network (implemented by linear layers) is pre-trained. We further propose to employ a Graph Convolutional Network (GCN) to learn the data similarity based on prior pairwise information, and make clear the training direction of the latent variable. Clustering label assignment and feature representation can be optimized by clustering loss alone. Unlike previous methods that only use pairwise information as a constraint in neural network, this architecture can make full use of pairwise information and capture similarities from it, optimizing the entire network for better clustering performance. We conduct many experiments on four popular benchmark datasets of images using the same set of learning rates, and it is shown that our SGDEC achieves a significant improvement over the new single-view algorithms, even better than the latest multi-view methods.</p>