We investigate weakly-supervised image parsing, i.e., assigning class labels to image regions by using image-level labels only. Existing studies pay main attention to the formulation of the weakly-supervised learning problem, i.e., how to propagate class labels from images to regions given an affinity graph of regions. Notably, however, the affinity graph of regions, which is generally constructed in relatively simpler settings in existing methods, is of crucial importance to the parsing performance due to the fact that the weakly-supervised parsing problem cannot be solved within a single image, and that the affinity graph enables label propagation among multiple images. In order to embed more semantics into the affinity graph, we propose novel criteria by exploiting the weak supervision information carefully, and develop two graphs: L1 semantic graph and k-NN semantic graph. Experimental results demonstrate that the proposed semantic graphs not only capture more semantic relevance, but also perform significantly better than conventional graphs in image parsing.