Segmenting histology images into diagnostically relevant regions is\nimperative to support timely and reliable decisions by pathologists. To this\nend, computer-aided techniques have been proposed to delineate relevant regions\nin scanned histology slides. However, the techniques necessitate task-specific\nlarge datasets of annotated pixels, which is tedious, time-consuming,\nexpensive, and infeasible to acquire for many histology tasks. Thus,\nweakly-supervised semantic segmentation techniques are proposed to utilize weak\nsupervision that is cheaper and quicker to acquire. In this paper, we propose\nSegGini, a weakly supervised segmentation method using graphs, that can utilize\nweak multiplex annotations, i.e. inexact and incomplete annotations, to segment\narbitrary and large images, scaling from tissue microarray (TMA) to whole slide\nimage (WSI). Formally, SegGini constructs a tissue-graph representation for an\ninput histology image, where the graph nodes depict tissue regions. Then, it\nperforms weakly-supervised segmentation via node classification by using\ninexact image-level labels, incomplete scribbles, or both. We evaluated SegGini\non two public prostate cancer datasets containing TMAs and WSIs. Our method\nachieved state-of-the-art segmentation performance on both datasets for various\nannotation settings while being comparable to a pathologist baseline.\n