Multigraph Message Passing with Bi-Directional Multi-Edge Aggregations

TL;DR

MEGA-GNN tackles multigraph learning by introducing a two-stage message passing framework that first aggregates parallel edges via artificial nodes and then aggregates messages across distinct neighbors, preserving edge-level information and multigraph topology. It proves permutation equivariance and, under a context-driven strict edge ordering, universality, addressing limitations of prior multigraph GNNs which either break equivariance or collapse edge structure. Empirically, MEGA-GNN achieves notable improvements on illicit-transaction detection and phishing-account classification, outperforming state-of-the-art baselines and demonstrating the practical value of edge-aware, bi-directional aggregation. This work advances GNN expressivity on complex multigraph data with potential impact across finance and security domains by enabling richer edge-feature propagation while maintaining principled symmetry properties.

Abstract

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 multigraphs, 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 of messages from distinct neighbors. We show that MEGA-GNN is not only permutation equivariant but also universal given a strict total ordering on the edges. Experiments show that MEGA-GNN significantly outperforms state-of-the-art solutions by up to 13\% on Anti-Money Laundering datasets and is on par with their accuracy on real-world phishing classification datasets in terms of minority class F1 score.

Figures (6)

• Figure 1: Directed multigraph port numbering of Multi-GNN (egressy2024provably).
• Figure 2: Illustration of ADAMM adamm
• Figure 3: Comparison of two-stage and single-stage aggregation strategies for multigraphs. The left panel illustrates a sample multigraph. The center panel depicts the two-stage aggregation process, wherein the first stage aggregates parallel edges, followed by a second stage node-level aggregation. The right panel shows the single-stage node-level aggregation scheme commonly employed by standard GNNs, which aggregates all edges, including the parallel edges, at once.
• Figure 4: Illustration of Multi-Edge Aggregation using artificial nodes in a multigraph. (a) A multigraph with parallel edges $e_{ij1}, e_{ij2}, e_{ij3}$ between the nodes $i$ and $j$. (b) Artificial nodes positioned between adjacent pairs of nodes to handle the aggregation of parallel edges. First, the information from the parallel edges are aggregated into some embedding vectors in the artificial nodes, and then the destination node performs a node-level aggregation on these embeddings. (c) The reverse message passing mechanism. In directed multigraphs, reverse edges are created in the reverse direction of the original edges, and then additional artificial nodes are introduced to handle the aggregation of these reverse edges. Separate message computations are performed to handle the original and reversed edges. The result is a bi-directional multigraph message passing solution.
• Figure 5: Throughput (transactions/sec) and minority-class F1 score (right) comparisons between MEGA-GNN and Multi-GNN variants across AML Small HI, AML Small LI, and ETH datasets.

Theorems & Definitions (7)

• Proposition 2.1
• Definition 3.1
• Definition 3.2
• Definition 3.3
• Theorem 3.1
• Lemma 3.1
• Theorem 3.2