GraphTrials: Visual Proofs of Graph Properties

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

arXiv · 2409.02907

GraphTrials: Visual Proofs of Graph Properties

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

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.HC

Keep this discovery

BibTeX RIS

Henry Förster, Felix Klesen, Tim Dwyer, Peter Eades, Seok-Hee Hong, Stephen G. Kobourov, Giuseppe Liotta, Kazuo Misue, Fabrizio Montecchiani, Alexander Pastukhov, Falk Schreiber. 2024-09-04. GraphTrials: Visual Proofs of Graph Properties. https://arxiv.org/abs/2409.02907

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

ShellVis: Sandboxed Live Programming for Shell Scripts

Live programming provides visibility to programmers by running and tracing programs as they are edited. However, for programs with potentially harmful side effects, liveness can turn mistakes into disasters. We propose enabling live programming in environments with side effects via sandboxing: confining effects to a simulation of the true environment. We apply sandboxed live programming in the challenging context of shell scripting: a ubiquitous and powerful---yet notoriously opaque and error-prone---tool. ShellVis provides line-by-line feedback on a shell script's run-time behavior, with file operations sandboxed via a safe overlay of the file system. A qualitative user evaluation finds ShellVis to be helpful to participants, replacing tedious existing practices and instilling confidence. Participant responses also reveal areas for future research, particularly bridging the gulf of execution alongside the gulf of evaluation. ShellVis serves as a case study of how sandboxing can bring live-programming techniques into the many real-world programming contexts where side effects are important.

cs.HC↗

arXiv2026

Visual-Motion-Induced Modulation of Pedestrian Trajectories Using Spatially Distributed Multi-Display Signage in Public Spaces

Multi-display signage (MDS), now ubiquitous in urban environments, has the potential to influence human behavior and experience in public spaces. However, despite its unique capability to present spatially distributed dynamic visual stimuli, its current use is mainly limited to advertising. In this study, we propose a perception-based approach for laterally modulating pedestrian trajectories as a nonverbal means of guiding pedestrians in public spaces. The approach is motivated by vection, the illusion of self-motion, and uses laterally moving monochrome stripes, a standard stimulus in vection research, presented across spatially distributed displays to elicit postural responses that may bias pedestrian trajectories. We evaluated the approach through a controlled laboratory experiment and a real-world field deployment involving actual pedestrian flows in a national museum. The laboratory experiment examined whether the MDS setup induced trajectory shifts in the direction predicted by prior research on the behavioral effects of vection. The field deployment investigated whether comparable effects would emerge in aggregate pedestrian behavior during unconstrained movement under conditions closer to those of urban public spaces. In the laboratory, full-screen motion significantly biased walking trajectories in the direction of visual motion, whereas partial-stripe motion produced no significant directional effect. In the field deployment, opposing full-screen motion conditions produced direction-consistent differences in aggregate pedestrian positions. The field results, observed despite the substantial variability in real-world pedestrian flows, extend the controlled laboratory findings and provide ecologically valid evidence supporting practical MDS-based pedestrian modulation in public settings. The results further suggest that sufficient visual-motion coverage may be important.

cs.HC↗

arXiv2026

How AI Coders Discuss, Disagree, and Reach Consensus: Challenges and Opportunities for LLM-Based Qualitative Coding

The utility of AI in multi-coder qualitative coding has been widely discussed, yet little empirical evidence exists to delineate the contexts in which it performs reliably. We address this gap by quantifying the effectiveness of multi-agent LLM coding across varied qualitative datasets, revealing key contextual and structural factors that mediate coding outcomes. We developed a literature-informed baseline pipeline that enables AI agents to independently code, debate, and reconcile disagreements. Results revealed that coding accuracy depends on factors such as codebook length, qualitative data similarity, and agent disagreement. Notably, intense and unresolved debates between agents led to higher accuracy. Our analysis showed that while LLMs emulate many human discussion behaviors, they lack adaptive responsiveness to context. From these findings, we offer design recommendations for building automated coding systems. Our open-source AI discussion dataset and methodological framework lay the groundwork for advancing the design of AI-mediated automated thematic analysis.

cs.HC↗