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GraphTrials: Visual Proofs of Graph Properties

Authors Henry Förster , Felix Klesen , Tim Dwyer , Peter Eades , Seok-Hee Hong , Stephen G. Kobourov , Giuseppe Liotta , Kazuo Misue , Fabrizio Montecchiani , Alexander Pastukhov , Falk Schreiber

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Author Details

Henry Förster
  • Department of Computer Science, University of Tübingen, Germany
Felix Klesen
  • Institute of Computer Science, University of Würzburg, Germany
Tim Dwyer
  • Faculty of Information Technology, Monash University, Australia
Peter Eades
  • School of Computer Science, The University of Sydney, Australia
Seok-Hee Hong
  • School of Computer Science, The University of Sydney, Australia
Stephen G. Kobourov
  • Department of Computer Science, University of Arizona, Tucson, AZ, USA
Giuseppe Liotta
  • Department of Engineering, University of Perugia, Italy
Kazuo Misue
  • Department of Computer Science, University of Tsukuba, Japan
Fabrizio Montecchiani
  • Department of Engineering, University of Perugia, Italy
Alexander Pastukhov
  • Department of Psychology, University of Bamberg, Germany
Falk Schreiber
  • Department of Computer Science, University of Konstanz, Germany

Acknowledgements

This work was initiated at Dagstuhl seminar 23051 "Perception in Network Visualization". We thank the organizers for making this fruitful interdisciplinary exchange possible and all participants for interesting discussions and insights during the seminar week.

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Henry Förster, Felix Klesen, Tim Dwyer, Peter Eades, Seok-Hee Hong, Stephen G. Kobourov, Giuseppe Liotta, Kazuo Misue, Fabrizio Montecchiani, Alexander Pastukhov, and Falk Schreiber. GraphTrials: Visual Proofs of Graph Properties. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.GD.2024.16

Abstract

Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based question-answering tools, issues of trustworthiness and explainability of generated answers motivate a greater role for visualization. In the context of graphs, we see the need for visualizations that can convince a critical audience that an assertion about the graph under analysis is valid. The requirements for such representations that convey precisely one specific graph property are quite different from standard network visualization criteria which optimize general aesthetics and readability. In this paper, we aim to provide a comprehensive introduction to visual proofs of graph properties and a foundation for further research in the area. We present a framework that defines what it means to visually prove a graph property. In the process, we introduce the notion of a visual certificate, that is, a specialized faithful graph visualization that leverages the viewer’s perception, in particular, pre-attentive processing (e. g. via pop-out effects), to verify a given assertion about the represented graph. We also discuss the relationships between visual complexity, cognitive load and complexity theory, and propose a classification based on visual proof complexity. Finally, we provide examples of visual certificates for problems in different visual proof complexity classes.

Subject Classification

ACM Subject Classification
  • Human-centered computing → Visualization theory, concepts and paradigms
  • Human-centered computing → Graph drawings
  • Human-centered computing → Information visualization
Keywords
  • Graph Visualization
  • Theory of Visualization
  • Visual Proof

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