This paper challenges the convention of using graph-theoretic shortest distance in stress-based graph drawing. We propose a new paradigm based on resistance distance, derived from the graph Laplacian's spectrum, which better captures global graph structure. This approach overcomes theoretical and computational limitations of traditional methods, as resistance distance admits a natural isometric embedding in Euclidean space. Our experiments demonstrate improved neighborhood preservation and cluster faithfulness. We introduce Omega, a linear-time graph drawing algorithm that integrates a fast resistance distance embedding with random node-pair sampling for Stochastic Gradient Descent (SGD). This comprehensive random sampling strategy, enabled by efficient pre-computation of resistance distance embeddings, is more effective and robust than pivot-based sampling used in prior algorithms, consistently achieving lower and more stable stress values. The algorithm maintains $O(\vert E\vert)$ complexity for both weighted and unweighted graphs. Our work establishes a connection between spectral graph theory and stress-based layouts, providing a practical and scalable solution for network visualization.

Recent research revealed that embedding a node-link diagram in a flat torus avoids edge crossings, improves aesthetic metrics, and has advantages in tasks such as path tracking and understanding network structures. However, the effectiveness of torus layouts using graphs and the influence of the cell size, the size of the torus space used during torus layouts on the drawing results have not been investigated. In this study, we clarified that the optimal cell size that minimizes the stress of drawing results differs depending on the graph through computational experiments using benchmark graph data. Moreover, we uncovered that in graphs with enabled torus layouts, the stress function depending on the cell size, is close to an unimodal function. We focused on this unimodal property and proposed an algorithm to determine whether a torus is valid from the drawing results and the optimal cell size using the golden-section search. Reportedly, the aesthetic metrics of graphs with optimal cell sizes outperformed empirically used cell sizes through computational experiments.

Social networking services (SNSs) have become the main avenue, where people speak their thoughts. Accordingly, we can explore people's thoughts by analyzing topics in SNS. When do topics change? Do they ever come back? What do people mainly talk about? In this study, we design and propose a novel visual analytics system to answer these interesting questions. We abstract the topic per unit time as a point in a two-dimensional space through document embedding and dimensionality reduction techniques and provide supplemented charts that represent words appearing at a certain time and the time-series change of word occurrence over the entire period. We employ a novel text visualization technique, called semantic preserving word bubbles, to visualize words at a certain time. In addition, we demonstrate the effectiveness of our system using Twitter data about early COVID-19 trends in Japan. We propose our system to help users to explore and understand transitions in posted contents on SNS.

Group-in-a-box (GIB) is a graph-drawing method designed to facilitate the visualization of the group structure of a graph. GIB allows the user to simultaneously view group sizes and inter-and intra-group structures. Several GIB variants have been proposed in the literature; however, their advantages and disadvantages have not been studied from the perspective of human cognition. Therefore, herein, we used eye tracking analysis and user surveys to evaluate the user experience of four GIB variants: Squarified-Treemap GIB(ST-GIB), Croissant-and-Doughnut GIB (CD-GIB), Force-Directed GIB (FD-GIB), and Tree-Reordered GIB (TR-GIB). We found some trade-offs among the methods for each type of user task and that FD-GIB and TR-GIB are superior than the other variants. Although ST-GIB's results were good, links were difficult to read in this graph layout. Eye-tracking data was gathered to determine which elements in each visualization significantly affected user experience. The results of this study will promote the effective use of GIB to analyze networks such as social networks or web graphs.

Wet and dry biological data are potentially complementary. By visually integrating the initiation and developmental processes of organisms, we might reveal new causalities in biological data. Here we present an integrated visualization system for a causality network constructed from phenotypic developmental characters and their related scientific literature. To obtain the phenotypic characters, we applied bio-imaging informatics techniques to the data of wet experiments. The phenotypic character network was visually rendered in the CausalNet system, which provides both explanatory and verification visualization functions. Statistical analysis and scientific literature mining proved useful for determining the mechanisms underlying the phenotypic trait network. The validity of the system was confirmed in an application example and expert feedback on the developmental process of the nematode Caenorhabditis elegans. The discussed methodology is applicable to other multicellular organisms.

In most species, calcium waves in the oocyte are considered common phenomena in the activation of eggs. However, the mechanism of calcium waves has not yet been clarified. By collaborating with biologists studying Caenorhabditis elegans ( C. elegans ), which is widely used as a model organism, we observed that the following requirements must be satisfied to form a useful hypothesis based on calcium waves captured using high-speed in vivo imaging: (1) the ability to obtain an overview of how the calcium waves are propagated and (2) the ability to understand the propagation of waves in a narrow region. However, conventional visualization methods cannot satisfy these requirements simultaneously. Therefore, we propose a visual analytics system that allows users to understand and explore calcium wave images using cross-correlation analysis of the time-series data of the Ca 2+ fluorescence intensity at each point. The interface of this system comprises an overview visualization, a detail visualization, and user interactions to satisfy these requirements and realize exploratory visualization. Some views present an overview visualization that displays the clustering results of a directed graph calculated using cross-correlation analysis. These views enable the users to understand the overview of wave propagation, thereby helping users find a region of interest. The detail visualization shows the relationship between the region of interest and other areas. Furthermore, users can use the proposed system with overview-detail and brush-link exploration to assign meaning to the region of interest and construct a hypothesis for its role. In this paper, we demonstrate how the proposed visual analytics approach works and how new hypotheses can be formed using the analysis of C. elegans calcium waves.

Biclustering is a well-known approach for data mining, and it is applied in many fields, such as genome analyses, security services, and social network analyses. Biclustering finds bicliques contained in a bipartite graph. However, in real data, a biclique may lack several edges because of various reasons, such as errors. In this situation, traditional biclustering methods cannot find correct biclusters. A novel biclustering method that can analyze real data under uncertainty is needed. Quasi-biclique is a mathematical concept that represents incomplete bicliques. We propose the quasi-biclique edge concentration (QBEC) method, which is a visual analysis method for biclustering using quasi-biclique mining. QBEC includes visual representations and user interactions for quasi-bicliques. Quasi-bicliques contained in a bipartite graph are represented based on edge concentration. The incompleteness of a quasi-biclique is reflected in edge opacity. Users can interactively explore data by adjusting the incompleteness parameter of the quasi-biclique. We demonstrate the effectiveness of QBEC using real-world data.

Edge concentration in dense bipartite graphs is a technique for reducing the numbers of edges and edge crossings in graph drawings. The conventional method proposed by Newbery is designed to reduce the number of edge crossings; however, it does not always reduce the number of edges. Reducing the number of edges is also an important factor for improving the readability of graphs. However, no edge concentration method with the explicit purpose of minimizing the number of edges has previously been studied. In this study, we propose a novel, efficient heuristic method for minimizing the number of edges during edge concentration. We demonstrate the efficiency of the proposed method via a comparison using randomly generated graphs. We find that Newbery's method fails to reduce the number of edges when the number of vertices is large. By contrast, the proposed method achieves an average compression ratio of 47 to 82 percent for all generated graph groups. We also present a real-world application of the proposed method using a causality network of biological data.