Multigraph Message Passing with Bi-Directional Multi-Edge Aggregations

Graph Neural Networks (GNNs) have seen significant advances in recent years, yet their application to multigraphs, where parallel edges exist between the same pair of nodes, remains under-explored. Standard GNNs, designed for simple graphs, compute node representations by combining all connected edges at once, without distinguishing between edges from different neighbors. There are some GNN architectures proposed specifically for multigraph tasks, yet these architectures perform only node-level aggregation in their message-passing layers, which limits their expressive power. Furthermore, these approaches either lack permutation equivariance when a strict total edge ordering is absent, or fail to preserve the topological structure of the multigraph. To address all these shortcomings, we propose MEGA-GNN, a unified framework for message passing on multigraphs that can effectively perform diverse graph learning tasks. Our approach introduces a two-stage aggregation process in the message passing layers: first, parallel edges are aggregated, followed by a node-level aggregation that operates on aggregated messages from distinct neighbors. We show that MEGA-GNN supports permutation equivariance and invariance properties. We also show that MEGA-GNN is universal given a strict total order on the edges. Experiments on synthetic and real-world financial transaction datasets demonstrate that MEGA-GNN either significantly outperforms or is on par with the accuracy of state-of-the-art solutions.