Perception of Symmetries in Drawings of Graphs

Luca, Felice De; Kobourov, Stephen G.; Purchase, Helen C.

doi:10.1007/978-3-030-04414-5_31

Cited by 4 publications

(7 citation statements)

References 21 publications

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“…Symmetry perception in graphs was also investigated by de Luca et al [127]. An online study using data from 56 participants found that horizontal symmetry was considered most important, followed by vertical and then translational symmetry.…”

Section: A: Graph Classes and Topologymentioning

confidence: 98%

“…Summary: There seems to be a tendency to hierarchical drawings in a top-to-bottom style with straight links [123], [124], also identifying a geodesic-path behavior by using eye tracking, for example, to explore search and information processing tasks [125]. Symmetry is an important feature [126], [127] as well as outlines [128] and similarity [131]. For meta-properties, it seems that a multi-dimensional scaling layout was best [129].…”

Section: A: Graph Classes and Topologymentioning

confidence: 99%

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The State of the Art in Empirical User Evaluation of Graph Visualizations

et al. 2021

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While graph drawing focuses more on the aesthetic representation of node-link diagrams, graph visualization takes into account other visual metaphors making them useful for graph exploration tasks in information visualization and visual analytics. Although there are aesthetic graph drawing criteria that describe how a graph should be presented to make it faster and more reliably explorable, many controlled and uncontrolled empirical user studies flourished over the past years. The goal of them is to uncover how well the human user performs graph-specific tasks, in many cases compared to previously designed graph visualizations. Due to the fact that many parameters in a graph dataset as well as the visual representation of them might be varied and many user studies have been conducted in this space, a state-of-the-art survey is needed to understand evaluation results and findings to inform the future design, research, and application of graph visualizations. In this article, we classify the present literature on the topmost level into graph interpretation, graph memorability, and graph creation where the users with their tasks stand in focus of the evaluation, not the computational aspects. As another outcome of this work, we identify the white spots in this field and sketch ideas for future research directions.

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Section: A: Graph Classes and Topologymentioning

confidence: 98%

Section: A: Graph Classes and Topologymentioning

confidence: 99%

The State of the Art in Empirical User Evaluation of Graph Visualizations

et al. 2021

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“…In order to distinguish inputs of different sizes, we refer to layouts in our dataset as small or large based on the number of vertices, |V |. A small layout has |V | ∈ [5,8] -SmallSym: small reflective symmetric layout -SmallNonSym: non symmetric generated from SmallSym with random node positions -ReflectionalLarge: large reflective symmetric layouts with random axis of symmetry -NonSymLarge: non symmetric generated from ReflectionalLarge layouts -HorizontalLarge: large reflective symmetric layouts with a 0 degree axis of symmetry -VerticalLarge: large reflective symmetric layouts with a 90 degree axis of symmetry -RotationalLarge: rotational symmetric with random axes between 4 and 10 -TranslationalLarge: translational symmetric translated along x-axis…”

Section: Datasetsmentioning

confidence: 99%

“…We used the procedure for generating a graph and a reflectional symmetric layout with the "parallel lines" feature following the algotithm in [8] as follows. Given a graph with n 2 vertices, called a component, we assign to each vertex of the component positive random coordinates.…”

Section: Reflectional Layout Generationmentioning

confidence: 99%

“…In psychology, for example, studies on the impact of symmetry on humans show that the vertical symmetry in objects is perceived pre-attentively. A similar study conducted in the context of graph drawing also shows that the vertical symmetry in drawings of graphs is best perceived among all others [8]. In this context, algorithms to measure symmetries in graph drawings have been proposed although it has been shown that these measures do not always agree with what humans perceive as symmetric [34].…”

Section: Introductionmentioning

confidence: 98%

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Symmetry Detection and Classification in Drawings of Graphs

Luca¹,

Hossain²,

Kobourov³

2019

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Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and especially reflectional symmetries, are also important in drawings of graphs. Detecting and classifying symmetries can be very useful in algorithms that aim to create symmetric graph drawings and in this paper we present a machine learning approach for these tasks. Specifically, we show that deep neural networks can be used to detect reflectional symmetries with 92% accuracy. We also build a multi-class classifier to distinguish between reflectional horizontal, reflectional vertical, rotational, and translational symmetries. Finally, we make available a collection of images of graph drawings with specific symmetric features that can be used in machine learning systems for training, testing and validation purposes. Our datasets, best trained ML models, source code are available online.

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