Structure-Aware Simplification for Hypergraph Visualization (2407.19621v1)

Abstract: Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was developed allowing hypergraphs with thousands of hyperedges to be simplified and examined at different levels of detail. However, this approach is not guaranteed to eliminate all of the visual clutter caused by unavoidable overlaps. Furthermore, meaningful structures can be lost at simplified scales, making their interpretation unreliable. In this paper, we define hypergraph structures using the bipartite graph representation, allowing us to decompose the hypergraph into a union of structures including topological blocks, bridges, and branches, and to identify exactly where unavoidable overlaps must occur. We also introduce a set of topology preserving and topology altering atomic operations, enabling the preservation of important structures while reducing unavoidable overlaps to improve visual clarity and interpretability in simplified scales. We demonstrate our approach in several real-world applications.