Rethinking Graph Super-resolution: Dual Frameworks for Topological Fidelity

Abstract: Graph super-resolution, the task of inferring high-resolution (HR) graphs from low-resolution (LR) counterparts, is an underexplored yet crucial research direction that circumvents the need for costly data acquisition. This makes it especially desirable for resource-constrained fields such as the medical domain. While recent GNN-based approaches show promise, they suffer from two key limitations: (1) matrix-based node super-resolution that disregards graph structure and lacks permutation invariance; and (2) reliance on node representations to infer edge weights, which limits scalability and expressivity. In this work, we propose two GNN-agnostic frameworks to address these issues. First, Bi-SR introduces a bipartite graph connecting LR and HR nodes to enable structure-aware node super-resolution that preserves topology and permutation invariance. Second, DEFEND learns edge representations by mapping HR edges to nodes of a dual graph, allowing edge inference via standard node-based GNNs. We evaluate both frameworks on a real-world brain connectome dataset, where they achieve state-of-the-art performance across seven topological measures. To support generalization, we introduce twelve new simulated datasets that capture diverse topologies and LR-HR relationships. These enable comprehensive benchmarking of graph super-resolution methods.