GraphTrials: Visual Proofs of Graph Properties
Henry F\"orster, Felix Klesen, Tim Dwyer, Peter Eades, Seok-Hee Hong,, Stephen G. Kobourov, Giuseppe Liotta, Kazuo Misue, Fabrizio Montecchiani,, Alexander Pastukhov, Falk Schreiber

TL;DR
This paper introduces a framework for visual proofs of graph properties, emphasizing visual certificates that leverage perception to verify assertions, aiming to enhance trustworthiness and explainability in graph analysis.
Contribution
It defines the concept of visual proofs and certificates for graph properties, establishing a foundation for visual verification methods distinct from traditional visualization.
Findings
Introduces the notion of visual certificates for graph properties
Proposes a classification based on visual proof complexity
Provides examples across different complexity classes
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…
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