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Multivariate graphs unite two distinct data perspectives: a topological structure defined by nodes and edges, and attribute data associated with each node. Analyzing such graphs therefore requires reasoning across two complementary spaces. However, existing systems typically emphasize the analysis of one space at a time, focusing either on topology or on attributes. As a result, exploration, analysis, and pattern discovery that depend on their interaction remain difficult. In this paper, we present a technique for formalizing and inducing patterns in multivariate graphs, instantiated in the ZipLine visual analytics system. Its central contribution is a predicate formalism that represents structural properties, node attributes, and bounded neighborhood relations while ensuring deterministic evaluation and a finite search space. Building on this formalism, ZipLine provides a predicate-learning algorithm that induces logical expressions from analyst-defined selections across topology and attribute views by combining attribute filters, structural properties, and neighborhood criteria. This approach supports iterative analysis by enabling analysts to refine patterns through coordinated reasoning over topology and attributes. We demonstrate ZipLine through three case studies in energy infrastructure, cybersecurity, and drug discovery analysis. The results show that ZipLine enables expressive multivariate graph analysis through unified reasoning across topology and attributes.

Graphs are commonly visualized in 2D, where humans readily interpret spatial relationships, yet such layouts often distort higher-dimensional structure. We propose to embed graphs in high-dimensional space and search for informative 2D viewpoints that optimize aesthetic and readability metrics (e.g., edge crossings and angular resolution), enabled by a novel differentiable surrogate for edge crossings. Numerical experiments show that these viewpoints consistently outperform standard 2D layouts, and can even surpass methods explicitly designed to optimize these metrics. We further introduce DataFly, an interactive system for exploring multiple candidate viewpoints through seamless navigation. A usability study demonstrates that our approach reveals structural patterns that remain hidden in conventional 2D visualizations.

Compositing multiple visualizations into a coherent whole remains challenging due to the vast design space and the need to balance the coverage of task-relevant data insights (e.g., trends and outliers), perceptual clarity, and aesthetic quality. In this paper, we present VisPuzzle, a task-aware method that formulates visualization composition as a stepwise search problem over a composition graph. In this graph, nodes represent either data composition operations (e.g., union, join) or visual composition operations that determine component relationships, spatial arrangements, or component proportions, and edges encode feasible transitions between operations. We employ Monte Carlo Graph Search to efficiently identify high-quality composition candidates from this graph, guided by a reward function that balances task relevance, perceptual effectiveness, and aesthetic coherence. A use case and a user study show that the top-ranked candidates produced by VisPuzzle align closely with human judgments of composition quality, demonstrating its utility in supporting principled and scalable visualization composition.

Graph layout is a fundamental problem in graph visualization, where node placement directly affects the readability and interpretability of graph structures. Recent graph neural network (GNN)-based methods have shown promising performance in automatic graph layout generation, but they typically coordinate multiple aesthetic objectives through fixed optimization schemes or weighted loss combinations, making training sensitive to manually specified weights and costly under simultaneous multi-objective optimization. To address these challenges, we propose LayoutAgent, an agent-driven graph layout optimization framework that reformulates multi-objective layout learning as adaptive temporal scheduling. LayoutAgent combines Multi-Objective Aesthetic Graph Embedding (MAGE), enhanced by a Spatial Weighting Adaptation Network (SWAN), with a Phase-wise Multi-Objective Optimization (PMO) mechanism that activates one objective in each training phase. LayoutAgent-Online generates state-dependent schedules to determine the frequency and execution order of aesthetic objectives, while LayoutAgent-Offline distills the online scheduling behavior through LoRA fine-tuning to reduce repeated online LLM queries while preserving comparable scheduling behavior and layout quality. Experiments on the Rome benchmark and representative SuiteSparse graphs show that LayoutAgent achieves competitive layout quality across multiple aesthetic metrics, improves over representative fixed and stochastic scheduling policies, and reduces per-epoch computational cost compared with joint multi-objective optimization baselines.

Graph databases are increasingly adopted as alternatives to tabular, aggregation-focused data models used in business intelligence (BI) systems such as Tableau, Power BI, and Looker. They capture complex relationships between entities, processes, and events, enabling analysis of information propagation in networks. As a result, graph analysis is central to applications such as fraud detection, social influence analysis, and supply chain resilience. Despite these advantages, existing tools do not adequately support interactive analysis of graph databases. Tabular BI systems lack mechanisms for reasoning over nodes and edges, while graph databases require specialized query languages and fragmented workflows that hinder accessibility. We present GraphPolaris, a no-code Visual Analytics system that enables users to explore, analyze, and visualize graph databases without programming skills. At its core, GraphPolaris features the GraphPolaris Query Language (GPQL), a formal query grammar that facilitates flexible and composable graph queries, providing a formal foundation for analyzing relationships and graph patterns. GPQL serves as an intermediary between user interactions and the underlying database. Its formal foundation enables no-code query construction, database-agnostic query generation, and guarantees that every interaction produces a valid executable query. Informed by a formative user study, we designed the GraphPolaris interface and visualizations to lower technical barriers and foster iterative, collaborative exploration of complex networks. We evaluate GraphPolaris through two real-world case studies in telecommunications and supply-chain analysis and a 22-month-long formative mixed-method study, including a MILC-based assessment of its fit to analysts’ graph analytics workflows.

In the visual analysis of hierarchical data, a main challenge is comparing data attributes both within and between different levels of the hierarchy. Such tasks are typically addressed using aggregated data, where the attribute of a parent node is calculated from the attributes of its children. Our review of existing literature on visualization methods that encode the hierarchy implicitly (e.g., icicle plots, treemaps) shows that most approaches rely on additive aggregation. Proportional aggregation, where a parent is assigned a weighted average of the values of its children, remains unexplored although relevant in practice. We introduce stalactite plots, a visualization technique that displays proportional aggregation and supports visual value comparison. Our empirical evaluation (N=148, N=50) shows that, with some explanation, stalactite plots are as easily understood as established visualization techniques for hierarchical data. Furthermore, for large datasets, participants are faster and more accurate using our approach.

We investigate tasks that can be accomplished with unlabeled graphs, which are graphs with nodes that do not have persistent or semantically meaningful labels attached. New visualization techniques to represent unlabeled graphs have been proposed, but more understanding of unlabeled graph tasks is required before these techniques can be adequately evaluated. Some network visualization tasks apply to both labeled and unlabeled graphs, but many do not translate between these contexts. We propose a data abstraction model that distinguishes the Unlabeled context from the increasingly semantically rich Labeled, Attributed, and Augmented contexts. We filter tasks collected and gleaned from the literature according to our data abstraction and analyze the surfaced tasks, leading to a taxonomy of abstract tasks for unlabeled graphs. Our task taxonomy is organized according to the Target data under consideration, the Action intended by the user, and the Scope of the data at play. We show the descriptive power of this task abstraction by connecting to concrete examples from previous frameworks, and connecting these abstractions to real-world problems. To showcase the evaluative power of the taxonomy, we perform a preliminary assessment across 6 different network visualization idioms for each task. For each combination of task and visual encoding, we consider the effort required from viewers, the likelihood of task success, and how both factors vary between small-scale and large-scale graphs.