In this paper, we test whether Multimodal Large Language Models (MLLMs) can match human-subject performance in tasks involving the perception of properties in network layouts. Specifically, we replicate a human-subject experiment about perceiving quality (namely stress) in network layouts using GPT-4o, Gemini-2.5 and Qwen2.5. Our experiments show that giving MLLMs the same study information as trained human participants yields performance comparable to that of human experts and exceeds that of untrained non-experts. Additionally, we show that prompt engineering that deviates from the human-subject experiment can lead to better-than-human performance in some settings. Interestingly, like human subjects, the MLLMs seem to rely on visual proxies rather than computing the actual value of stress, indicating some sense or facsimile of perception. Explanations from the models are similar to those used by the human participants (e.g., an even distribution of nodes and uniform edge lengths).

Circular interfaces such as those found on smartwatches, automotive dashboards, cockpit instruments, or in radial visualizations pose unique challenges for placing readable labels. Traditional rectangular labeling methods waste screen space and create visual clutter on these constrained displays. In orbital boundary labeling, the labels (e.g., the features' names) are placed in an annulus-shaped orbit outside of the figure, and each label is connected to its feature using a short, crossing-free leader line. We contribute algorithms to compute two leader styles, orbital-radial and straight-line, for uniform and non-uniform label sizes, optimizing for crossing-free shortest leaders. We evaluate the model and the algorithms with computational experiments and a controlled user experiment. The user experiment reveals that both leader types exhibit similar accuracy, but straight-line leaders yield faster response times.

Recent advances in Large Language Models have led to Large Reasoning Models, which produce step-by-step reasoning traces. Such traces may offer insight into how models think, improving explainability and clarifying the underlying process. These traces, however, are often verbose and complex, making them cognitively demanding to comprehend. With this in mind, we propose ReTrace, an interactive system that structures and visualizes textual reasoning traces to support understanding. We use a validated reasoning taxonomy to produce structured reasoning data and investigate two types of interactive visualizations thereof. In a controlled human-subject study, the visualizations provided more accurate comprehension of the model's reasoning and less perceived effort than a raw text baseline. The results of this study could have design implications for making long and complex machine-generated reasoning processes more usable and transparent, an important step in AI explainability.

Set and network data co-occur frequently, with the sets representing node groupings and the network representing connections between node pairs. This paper investigates two different designs for jointly visualizing set and network data: HoopNet and LinearNet. HoopNet juxtaposes a hoop diagram with a circular network layout, whereas LinearNet juxtaposes a linear diagram with a linear network layout. We investigate two variations of each: a set-first and a network-first layout. Our human-subject studies show there is no difference between set-first and network-first optimization. However, participants achieved significantly higher accuracy with HoopNet, indicating it is a more effective visualization for set and network data than LinearNet.

Graph drawing concerns the algorithmic visualization of graphs. A good drawing of a graph is easy to read and facilitates solving tasks on the graph. Several properties have been identified to occur in good drawings of graphs. Such properties include a low number of crossings, large angles between edges, short edges, and depicting symmetries. Many of these properties are explicitly measurable metrics. This brings us to the insight that graph drawing can be seen as a game. In this paper, we study a single-player optimization game in which the player iteratively moves vertices of a straight-line graph drawing to reduce edge crossings. This game arose naturally from the automatic track of the Graph Drawing Challenge, where solutions are obtained by repeatedly performing local vertex movements. We formalize this process as a game with full information and investigate whether reinforcement learning can discover effective strategies for playing it. Our reinforcement-learning agent observes the local geometric and structural context of a vertex and selects a movement direction with the goal of reducing either the global or the local crossing number, that is, the total number of crossings or the maximum number of crossings per edge. We compare the resulting strategies to existing methods and established crossing-minimization heuristics on standard benchmark graphs. While our approach does not out-compete state-of-the-art methods for minimizing the global crossing number, it is competitive and often superior for minimizing the local crossing number.

We present an exploratory study on how people perceive visualizations of spatial social networks generated by edge bundling algorithms. Although these algorithms successfully minimize clutter in node-link diagrams, they do so through various methods that can sometimes create false connections between nodes. We conducted a qualitative experiment involving participants with technical expertise but no prior knowledge of edge bundling algorithms. Participants described their perceptions of both bundled and straight-line visualizations in open-ended tasks. Analysis of their annotations and transcripts revealed a general preference for bundled visualizations. However, when it came to false connections, participants tended to follow them in tightly bundled diagrams while also vocalizing that these drawings were more ambiguous. The routing of bundles influenced the perception of clusters and participants assigned more or fewer nodes to the clusters, depending on the routing of bundles. Participants’ unfamiliarity with the dataset led them to use analogies to describe the bundled drawings, potentially adding perceived semantic meaning to the data.

We propose a method for visualizing uncertain set systems, which differs from previous set visualization approaches that are based on certainty (an element either belongs to a set or not). Our method is inspired by storyline visualizations and parallel coordinate plots: (a) each element is represented by a vertical glyph, subdivided into bins that represent different levels of uncertainty; (b) each set is represented by an x-monotone curve that traverses element glyphs through the bins representing the level of uncertainty of their membership. Our implementation also includes optimizations to reduce visual complexity captured by the number of turns for the set curves and the number of crossings. Although several of the natural underlying optimization problems are NP-hard in theory (e.g., optimal element order, optimal set order), in practice, we can compute near-optimal solutions with respect to curve crossings with the help of a new exact algorithm for optimally ordering set curves within each element's bins. With these optimizations, the proposed method makes it easy to see set containment (the smaller set's curve is strictly below the larger set's curve). A brief design-space exploration using uncertain set-membership data, as well as multi-dimensional discrete data, shows the flexibility of the proposed approach.

Edge bundling algorithms can significantly improve the visualization of dense graphs by identifying and bundling together suitable groups of edges and thus reducing visual clutter. As such, bundling is often viewed as a post-processing step applied to a drawing, and the vast majority of edge bundling algorithms consider a graph and its drawing as input. A different way of thinking about edge bundling is to simultaneously optimize both the drawing and the bundling, which we investigate in this paper. We build on an earlier work where we introduced a novel algorithmic framework for bundling-aware graph drawing consisting of three main steps, namely Filter for a skeleton subgraph, Draw the skeleton, and Bundle the remaining edges against the drawing of the skeleton. We propose several alternative implementations and experimentally compare them against each other and the simple idea of first drawing the full graph and subsequently applying edge bundling to it. The experiments confirm that bundled drawings created by our Filter-Draw-Bundle framework outperform previous approaches according to metrics for edge bundling and graph drawing.

Biofabric is a novel method for network visualization, with promising potential to highlight specific network features. Recent studies emphasize the importance of staircase motifs - equivalent to fans or stars in node-link diagrams - within Biofabric. However, to effectively showcase these motifs, we need to formulate specialized layout algorithms. This paper introduces a method to compute optimal layouts for Biofabric, focusing on maximizing staircase formation. We present an Integer Linear Programming (ILP) model for this task and evaluate its performance in terms of scalability and output quality against a leading heuristic method, Degreecending. Our results demonstrate that the ILP approach identifies significantly more, and often longer, staircases compared to Degreecending, albeit with the trade-off of higher computation times. Our supplemental material, including a full copy of the paper, code, and results, is available on osf.io.

Schematic depictions in text books and maps often need to label specific point features with a text label. We investigate one variant of such a labeling, where the image contour is a circle and the labels are placed as circular arcs along the circumference of this circle. To map the labels to the feature points, we use orbital-radial leaders, which consist of a circular arc concentric with the image contour circle and a radial line to the contour. In this paper, we provide a framework, which captures various dimensions of the problem space as well as several polynomial time algorithms and complexity results for some problem variants.

In various scientific and industrial domains, analyzing multivariate spatial data, i.e., vectors associated with spatial locations, is common practice. To analyze those datasets, analysts may turn to methods such as Spatial Blind Source Separation (SBSS). Designed explicitly for spatial data analysis, SBSS finds latent components in the dataset and is superior to popular non-spatial methods, like PCA. However, when analysts try different tuning parameter settings, the amount of latent components complicates analytical tasks. Based on our years-long collaboration with SBSS researchers, we propose a visualization approach to tackle this challenge. The main component is UnDRground Tubes (UT), a general-purpose idiom combining ideas from set visualization and multidimensional projections. We describe the UT visualization pipeline and integrate UT into an interactive multiple-view system. We demonstrate its effectiveness through interviews with SBSS experts, a qualitative evaluation with visualization experts, and computational experiments. SBSS experts were excited about our approach. They saw many benefits for their work and potential applications for geostatistical data analysis more generally. UT was also well received by visualization experts. Our benchmarks show that UT projections and its heuristics are appropriate.

We introduce Hoop Diagrams, a new visualization technique for set data. Hoop Diagrams are a circular visualization with hoops representing sets and sectors representing set intersections. We present an interactive tool for drawing Hoop Diagrams and describe a user study comparing them with Linear Diagrams. The results show only small differences, with users answering questions more quickly with Linear Diagrams, but answering some questions more accurately with Hoop Diagrams. Interaction data indicates that those using set order and intersection highlighting were more successful at answering questions, but those who used other interactions had a slower response. The similarity in usability suggests that the diagram type should be chosen based on the presentation method. Linear Diagrams increase in the horizontal direction with the number of intersections, leading to difficulties fitting on a screen. Hoop Diagrams al-ways have a square aspect ratio.

Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via crossing-free leaders. We propose orbital boundary labeling as a new variant of the problem, in which (i) the figure is enclosed by a circular contour and (ii) the labels are placed as disjoint circular arcs in an annulus-shaped orbit around the contour. The algorithmic objective is to compute an orbital boundary labeling with the minimum total leader length. We identify several parameters that define the corresponding problem space: two leader types (straight or orbital-radial), label size and order, presence of candidate label positions, and constraints on where a leader attaches to its label. Our results provide polynomial-time algorithms for many variants and NP-hardness for others, using a variety of geometric and combinatorial insights.

Hive plots are a graph visualization style placing vertices on a set of radial axes emanating from a common center and drawing edges as smooth curves connecting their respective endpoints. In previous work on hive plots, assignment to an axis and vertex positions on each axis were determined based on selected vertex attributes and the order of axes was prespecified. Here, we present a new framework focusing on combinatorial aspects of these drawings to extend the original hive plot idea and optimize visual properties such as the total edge length and the number of edge crossings in the resulting hive plots. Our framework comprises three steps: (1) partition the vertices into multiple groups, each corresponding to an axis of the hive plot; (2) optimize the cyclic axis order to bring more strongly connected groups near each other; (3) optimize the vertex ordering on each axis to minimize edge crossings. Each of the three steps is related to a well-studied, but NP-complete computational problem. We combine and adapt suitable algorithmic approaches, implement them as an instantiation of our framework and show in a case study how it can be applied in a practical setting. Furthermore, we conduct computational experiments to gain further insights regarding algorithmic choices of the framework. The code of the implementation and a prototype web application can be found on OSF.

Real-world datasets often consist of quantitative and categorical variables. The analyst needs to focus on either kind separately or both jointly. We proposed a visualization technique tackling these challenges that supports visual cluster and set analysis. In this paper, we investigate how its visualization parameters affect the accuracy and speed of cluster and set analysis tasks in a controlled experiment. Our findings show that, with the proper settings, our visualization can support both task types well. However, we did not find settings suitable for the joint task, which provides opportunities for future research.

Edge bundling algorithms significantly improve the visualization of dense graphs by reducing the clutter of many edges visible on screen by bundling them together. As such, bundling is often viewed as a post-processing step applied to a drawing, and the vast majority of edge bundling algorithms consider a graph and its drawing as input. Another way of thinking about edge bundling is to simultaneously optimize both the drawing and the bundling. In this paper, we investigate methods to simultaneously optimize a graph drawing and its bundling. We describe an algorithmic framework which consists of three main steps, namely Filter, Draw, and Bundle. We then propose two alternative implementations and experimentally compare them against the state-of-the-art approach and the simple idea of drawing and subsequently bundling the graph. The experiments confirm that bundled drawings created by our framework outperform previous approaches according to standard quality metrics for edge bundling.

Boundary labeling is a technique in computational geometry used to label sets of features in an illustration. It involves placing labels along an axis-parallel bounding box and connecting each label with its corresponding feature using non-crossing leader lines. Although boundary labeling is well-studied, semantic constraints on the labels have not been investigated thoroughly. In this paper, we introduce grouping and ordering constraints in boundary labeling: Grouping constraints enforce that all labels in a group are placed consecutively on the boundary, and ordering constraints enforce a partial order over the labels. We show that it is NP-hard to find a labeling for arbitrarily sized labels with unrestricted positions along one side of the boundary. However, we obtain polynomial-time algorithms if we restrict this problem either to uniform-height labels or to a finite set of candidate positions. Furthermore, we show that finding a labeling on two opposite sides of the boundary is NP-complete, even for uniform-height labels and finite label positions. Finally, we experimentally confirm that our approach has also practical relevance.