Computational and memory costs restrict spectral techniques to rather small graphs, which is a serious limitation especially in video segmentation. In this paper, we propose the use of a reduced graph based on superpixels. In contrast to previous work, the reduced graph is reweighted such that the resulting segmentation is equivalent, under certain assumptions, to that of the full graph. We consider equivalence in terms of the normalized cut and of its spectral clustering relaxation. The proposed method reduces runtime and memory consumption and yields on par results in image and video segmentation. Further, it enables an efficient data representation and update for a new streaming video segmentation approach that also achieves state-of-the-art performance.