HyDRA: Lossless Hypergraph Summarization via Co-Clustering

Abstract: Hypergraphs are a powerful representation for higher-order interactions but their scale and complexity pose significant data management and analysis challenges. While summarization techniques are widely used to distill simple graphs, lossless summarization for hypergraphs remains unexplored. We introduce HyDRA, the first formal framework for lossless summarization of weighted hypergraphs. In our framework, a summary is a new weighted hypergraph composed of supernodes (groups of nodes) and superhyperedges (groups of hyperedges), paired with a correction table for exact reconstruction. By establishing a conceptual link to co-clustering, we design an efficient, parameter-free greedy algorithm that iteratively merges node and hyperedge clusters to minimize a novel storage-aware cost function. HyDRA employs an incremental update strategy to prevent the costly recomputation of the correction table at each step. Extensive experiments demonstrate that \our achieves a substantial reduction in storage cost (80-93% in some settings, depending on the hypergraph characteristics). Because the resulting summaries are themselves hypergraphs, they can be queried directly, providing fast and accurate approximate answers for various connectivity and centrality queries, and accelerating downstream tasks such as influence maximization.