In recent years, graph convolution networks (GCN) have been proposed as semi-supervised learning approaches. In this paper, we introduce a new objective function to train a GCN in order to adapt it in unsupervised learning context. More precisely, we propose a loss function composed only of unsupervised terms, the first term is the kernel k-means objective function used to capture the shared features information between nodes, and the second is a regularization term that imposes the smoothness of the predicted clusters of the whole data. Thanks to the proposed objective function, we are able to keep the advantages of the classical semi-supervised GCN, while using it in an unsupervised way. Experiments on benchmark datasets show that our proposed unsupervised GCN achieves superior performance compared to state-of-the-art clustering algorithms.