Six methods for transforming layered hypergraphs to apply layered graph layout algorithms

Hypergraphs are a generalization of graphs in which edges (hyperedges) can connect more than two vertices—as opposed to ordinary graphs where edges involve only two vertices. Hypergraphs are a fairly common data structure but there is little consensus on how to visualize them. To optimize a hypergra...

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Bibliographic Details
Published in:Computer graphics forum Vol. 41; no. 3; pp. 259 - 270
Main Authors: Di Bartolomeo, Sara, Pister, Alexis, Buono, Paolo, Plaisant, Catherine, Dunne, Cody, Fekete, Jean‐Daniel
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.06.2022
Wiley
Series:EuroVis 2022 - Conference Proceedings
Subjects:
Algorithms
Apexes
CCS Concepts
Computer Science
Data structures
Graph theory
Graphs
Human-Computer Interaction
Human‐centered computing → Graph drawings
Layouts
Readability
Transformations
Visualization theory, concepts and paradigms
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:Hypergraphs are a generalization of graphs in which edges (hyperedges) can connect more than two vertices—as opposed to ordinary graphs where edges involve only two vertices. Hypergraphs are a fairly common data structure but there is little consensus on how to visualize them. To optimize a hypergraph drawing for readability, we need a layout algorithm. Common graph layout algorithms only consider ordinary graphs and do not take hyperedges into account. We focus on layered hypergraphs, a particular class of hypergraphs that, like layered graphs, assigns every vertex to a layer, and the vertices in a layer are drawn aligned on a linear axis with the axes arranged in parallel. In this paper, we propose a general method to apply layered graph layout algorithms to layered hypergraphs. We introduce six different transformations for layered hypergraphs. The choice of transformation affects the subsequent graph layout algorithm in terms of computational performance and readability of the results. Thus, we perform a comparative evaluation of these transformations in terms of number of crossings, edge length, and impact on performance. We also provide two case studies showing how our transformations can be applied to real‐life use cases. A copy of this paper with all appendices and supplemental material is available at osf.io/grvwu.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.14538