We present a weakly-supervised approach to semantic segmentation. The goal is to assign pixel-level labels given only partial information, for example, image-level labels. This is an important problem in many application scenarios where it is difficult to get accurate segmentation or not feasible to obtain detailed annotations. The proposed approach starts with an initial coarse segmentation, followed by a spectral clustering approach that groups related image parts into communities. A community-driven graph is then constructed that captures spatial and feature relationships between communities while a label graph captures correlations between image labels. Finally, mapping the image level labels to appropriate communities is formulated as a convex optimization problem. The proposed approach does not require location information for image level labels and can be trained using partially labeled datasets. Compared to the state-of-the-art weakly supervised approaches, we achieve a significant performance improvement of 9% on MSRC-21 dataset and 11% on LabelMe dataset, while being more than 300 times faster.