Graph neural networks (GNNs) have become effective learning techniques for many downstream network mining tasks including node and graph classification, link prediction, and network reconstruction. However, most GNN methods have been developed for homogeneous networks with only a single type of node and edge. Heterogeneous graphs are vital because they naturally model complex, real-world systems by representing diverse types of entities and the multiple kinds of relationships connecting them, which is essential for tasks like social network analysis, biological network mapping, and cybersecurity applications. To address these gaps, this work introduces a multiplex graph neural network for heterogeneous graphs. To model heterogeneity, we represent graphs as multiplex networks consisting of a set of layer graphs and a coupling graph that links node instantiations across multiple layers. We parameterize layer-specific representations of nodes and design a novel coupling attention mechanism that models the importance of multi-relational contexts for different types of nodes and edges in heterogeneous graphs. We further develop two complementary coupling structures: node invariant coupling suitable for node- and graph-level tasks, and node equivariant coupling suitable for link-level tasks. We conduct extensive experiments on real-world datasets for link prediction in both transductive and inductive contexts and for graph classification that demonstrate the superior performance of muxGNN over state-of-the-art heterogeneous GNNs. In addition, we show that muxGNN's coupling attention discovers interpretable connections betweendifferent relations in heterogeneous networks.
