Many neural network models have been proposed that operate directly on graph data structures. Existing methods are able to produce per-node feature embeddings for classification and regression and differ mainly in the methods by which they pass messages and gather features from node neighbourhoods. While learning from graph topology in this way has been explored well, the process of learning to modify graph topology in a semantically meaningful manner has received less attention. This work explores learnable reductions of graph topology by augmenting conventional graph representations and graph network models with the ability to merges together, while remaining fully-differentiable. The resulting framework is able to learn image segmentation using only merge operations, and is theoretically applicable to a large variety of problem domains where semantic reduction of graph data is desired.