Title: Fully Convolutional Graph Neural Networks using Bipartite Graph Convolutions. Abstract: Graph neural networks have been adopted in numerous applications ranging from learning relational representations to modeling data on irregular domains such as point clouds, social graphs, and molecular structures. Though diverse in nature, graph neural network architectures remain limited by the graph convolution operator whose input and output graphs must have the same structure. With this restriction, representational hierarchy can only be built by graph convolution operations followed by non-parameterized pooling or expansion layers. This is very much like early convolutional network architectures, which later have been replaced by more effective parameterized strided and transpose convolution operations in combination with skip connections. In order to bring a similar change to graph convolutional networks, here we introduce the bipartite graph convolution operation, a parameterized transformation between different input and output graphs. Our framework is general enough to subsume conventional graph convolution and pooling as its special cases and supports multi-graph aggregation leading to a class of flexible and adaptable network architectures, termed BiGraphNet. By replacing the sequence of graph convolution and pooling in hierarchical architectures with a single parametric bipartite graph convolution, (i) we answer the question of whether graph pooling matters, and (ii) accelerate computations and lower memory requirements in hierarchical networks by eliminating pooling layers. Then, with concrete examples, we demonstrate that the general BiGraphNet formalism (iii) provides the modeling flexibility to build efficient architectures such as graph skip connections, and autoencoders.