Scalable Hypergraph Visualization

Peter D Oliver, Eugene Zhang, Yue Zhang

Room: 105

2023-10-25T05:45:00ZGMT-0600Change your timezone on the schedule page
Exemplar figure, described by caption below
We present a scalable layout optimization framework for polygon visualizations of hypergraphs. Our framework achieves near-optimal polygon layouts for large hypergraphs (left) by first iteratively applying vertex and hyperedge-based simplification operations to scale down the input hypergraph. The coarsest simplified scale is determined by some user-specified criteria (right). After the layout of this simplified scale is optimized, the applied operations are iteratively inverted, and the layout is refined at each intermediate scale until the original scale is reached. An example of an intermediate scale is also shown (middle).
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Hypergraph visualization, scalable visualization, polygon layout, hypergraph embedding, primal-dual visualization


Hypergraph visualization has many applications in network data analysis. Recently, a polygon-based representation for hypergraphs has been proposed with demonstrated benefits. However, the polygon-based layout often suffers from excessive self-intersections when the input dataset is relatively large. In this paper, we propose a framework in which the hypergraph is iteratively simplified through a set of atomic operations. Then, the layout of the simplest hypergraph is optimized and used as the foundation for a reverse process that brings the simplest hypergraph back to the original one, but with an improved layout. At the core of our approach is the set of atomic simplification operations and an operation priority measure to guide the simplification process. In addition, we introduce necessary definitions and conditions for hypergraph planarity within the polygon representation. We extend our approach to handle simultaneous simplification and layout optimization for both the hypergraph and its dual. We demonstrate the utility of our approach with datasets from a number of real-world applications.