Deep clustering is a promising technique for speech separation that is crucial to speech communication, acoustic target detection, acoustic enhancement and speech recognition. In the study of monophonic speech separation, the problem is that the decrease in separation and generalization performance of the model in the case of reducing the variety of the training data set. In this paper, we propose a comprehensive deep clustering framework that construction the structural speech data based on GCN, named graph deep clustering (GDC) to further improve the separation performance of the separation model. In particular, embedding features are transformed into graph-structured data, and the speech separation mask is achieved by clustering these graph-structured data. Graph structural information aggregates nodes within a class, which makes feature representations conducive to clustering. Experimental results demonstrate that the proposed scheme can improve the clustering performance. The SDR of the separated speech is improved by about 1.2 dB, and the clustering accuracy is improved by 15%. We also use the perceptually motivated objective measures for the evaluation of audio source separation to score the speech quality. The target speech quality and the overall perceptual score are improved by 10.7% compared with other speech separation algorithms. INDEX TERMS Construction of graph-structured data, deep clustering, graph convolutional filter, speech separation.