A storyline visualization shows interactions between characters over time. Each character is represented by an x-monotone curve. Time is mapped to the x-axis, and groups of characters that interact at a particular point t in time must be ordered consecutively in the y-dimension at x = t. The predominant objective in storyline optimization so far has been the minimization of crossings between (blocks of) characters. Building on this work, we investigate another important, but less studied quality criterion, namely the minimization of wiggle, i.e., the amount of vertical movement of the characters over time. Given a storyline instance together with an ordering of the characters at any point in time, we show that wiggle count minimization is NP-complete. In contrast, we provide algorithms based on mathematical programming to solve linear wiggle height minimization and quadratic wiggle height minimization efficiently. Finally, we introduce a new method for routing character curves that focuses on keeping distances between neighboring curves constant as long as they run in parallel. We have implemented our algorithms, and we conduct a case study that explores the differences between the three optimization objectives. We use existing benchmark data, but we also present a new use case for storylines, namely the visualization of rolling stock schedules in railway operation.

Graphs are drawn for various purposes, and drawings are meant to display various features of a graph (such as planarity, Hamiltonicity). Still, there is a long history in measuring the quality of a graph drawing. Most of the metrics that have been implemented and used in large studies assume that graphs are drawn straight-line. Most of the studies use randomly generated graphs or one of very few existing benchmark sets that consist of graphs with a specific technical background (e.g., telecommunication networks). In this paper, we extend ten commonly used metrics to node-link diagrams where edges can be curves or polygonal chains. We implement these measures and use them to evaluate a new collection of graph drawings that we have extracted from 27 proceedings of the Graph Drawing conference using an automated pipeline. We compare the "metrics landscape" of our new benchmark set, the GD-collection-v1, which seems to mostly contain manually drawn graphs, to the metric landscape of a benchmark set with randomly generated graphs and computer-generated straight-line drawings that has been used in a recent study [Mooney et al.; PacificVis 2024]. Comparing the GD-collection-v1 with the Mooney at al. dataset reveals a distinct metrics landscape: GD drawings come from much smaller graphs (median vertex number 11 vs. 48) and therefore attain higher medians on most readability metrics. For example, Neighbourhood Preservation (0.5 vs. 0.239) is markedly higher in the GD-collection-v1. We also find that a large proportion of extracted drawings contain curved and/or polygonal edges (57%), motivating the extended metric definitions.

Egocentric networks, often visualized as node-link diagrams, portray the complex relationship (link) dynamics between an entity (node) and others. However, common analytics tasks are multifaceted, encompassing interactions among four key aspects: strength, function, structure, and content. Current node-link visualization designs may fall short, focusing narrowly on certain aspects and neglecting the holistic, dynamic nature of egocentric networks. To bridge this gap, we introduce SpreadLine, a novel visualization framework designed to enable the visual exploration of egocentric networks from these four aspects at the microscopic level. Leveraging the intuitive appeal of storyline visualizations, SpreadLine adopts a storyline-based design to represent entities and their evolving relationships. We further encode essential topological information in the layout and condense the contextual information in a metro map metaphor, allowing for a more engaging and effective way to explore temporal and attribute-based information. To guide our work, with a thorough review of pertinent literature, we have distilled a task taxonomy that addresses the analytical needs specific to egocentric network exploration. Acknowledging the diverse analytical requirements of users, SpreadLine offers customizable encodings to enable users to tailor the framework for their tasks. We demonstrate the efficacy and general applicability of SpreadLine through three diverse real-world case studies (disease surveillance, social media trends, and academic career evolution) and a usability study.