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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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
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Abstract	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.
AbstractList	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. 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.
Author	Di Bartolomeo, Sara Fekete, Jean‐Daniel Plaisant, Catherine Pister, Alexis Buono, Paolo Dunne, Cody
Author_xml	– sequence: 1 givenname: Sara orcidid: 0000-0001-9517-3526 surname: Di Bartolomeo fullname: Di Bartolomeo, Sara organization: Northeastern University – sequence: 2 givenname: Alexis orcidid: 0000-0002-2817-020X surname: Pister fullname: Pister, Alexis organization: Université Paris‐Saclay, CNRS, Inria, Orsay – sequence: 3 givenname: Paolo orcidid: 0000-0002-1421-3686 surname: Buono fullname: Buono, Paolo organization: University of Bari – sequence: 4 givenname: Catherine orcidid: 0000-0003-4049-5848 surname: Plaisant fullname: Plaisant, Catherine organization: University of Maryland – sequence: 5 givenname: Cody orcidid: 0000-0002-1609-9776 surname: Dunne fullname: Dunne, Cody organization: Northeastern University – sequence: 6 givenname: Jean‐Daniel orcidid: 0000-0003-3770-8726 surname: Fekete fullname: Fekete, Jean‐Daniel organization: Université Paris‐Saclay, CNRS, Inria, Orsay
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Copyright	2022 The Author(s) Computer Graphics Forum © 2022 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2022 The Eurographics Association and John Wiley & Sons Ltd. Distributed under a Creative Commons Attribution 4.0 International License
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Snippet	Hypergraphs are a generalization of graphs in which edges (hyperedges) can connect more than two vertices—as opposed to ordinary graphs where edges involve... Hypergraphs are a generalization of graphs in which edges (hyperedges) can connect more than two vertices—as opposed to ordinary graphs where edges involve... Hypergraphs are a generalization of graphs in which edges (hyperedges) can connect more than two vertices-as opposed to ordinary graphs where edges involve...
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SubjectTerms	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
Title	Six methods for transforming layered hypergraphs to apply layered graph layout algorithms
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