In multiview learning, it is essential to assign a reasonable weight to each view according to its importance. Thus, for multiview clustering task, a wise and elegant method should achieve clustering multiview data while learning the view weights. In this paper, we address this problem by exploring a Laplacian rank constrained graph, which can be approximately as the centroid of the built graph for each view with different confidences. We start our work with a natural thought that the weights can be learned by introducing a hyperparameter. By analyzing the weakness of it, we further propose a new multiview clustering method which is totally self-weighted. Furthermore, once the target graph is obtained in our models, we can directly assign the cluster label to each data point and do not need any postprocessing such as $K$-means in standard spectral clustering. Evaluations on two synthetic datasets prove the effectiveness of our methods. Compared with several representative graph-based multiview clustering approaches on four real-world datasets, experimental results demonstrate that the proposed methods achieve the better performances and our new clustering method is more practical to use.