A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., non-hierarchical edges, together. We realize this as follows. We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a B-spline curve, toward the polyline defined by the path via the inclusion edges from one node to another. This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques. We illustrate our technique by providing example visualizations and discuss the results based on an informal evaluation provided by potential users of such visualizations.

Graphs depicted as node-link diagrams are widely used to show relationships between entities. However, nodelink diagrams comprised of a large number of nodes and edges often suffer from visual clutter. The use of edge bundling remedies this and reveals high-level edge patterns. Previous methods require the graph to contain a hierarchy for this, or they construct a control mesh to guide the edge bundling process, which often results in bundles that show considerable variation in curvature along the overall bundle direction. We present a new edge bundling method that uses a self-organizing approach to bundling in which edges are modeled as flexible springs that can attract each other. In contrast to previous methods, no hierarchy is used and no control mesh. The resulting bundled graphs show significant clutter reduction and clearly visible high-level edge patterns. Curvature variation is furthermore minimized, resulting in smooth bundles that are easy to follow. Finally, we present a rendering technique that can be used to emphasize the bundling.

We propose a visual analytics approach for the exploration and analysis of dynamic networks. We consider snapshots of the network as points in high-dimensional space and project these to two dimensions for visualization and interaction using two juxtaposed views: one for showing a snapshot and one for showing the evolution of the network. With this approach users are enabled to detect stable states, recurring states, outlier topologies, and gain knowledge about the transitions between states and the network evolution in general. The components of our approach are discretization, vectorization and normalization, dimensionality reduction, and visualization and interaction, which are discussed in detail. The effectiveness of the approach is shown by applying it to artificial and real-world dynamic networks.

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We provide a novel visualization method for the comparison of hierarchically organized data. Our technique visualizes a pair of hierarchies that are to be compared and simultaneously depicts how these hierarchies are related by explicitly visualizing the relations between matching subhierarchies. Elements that are unique to each hierarchy are shown, as well as the way in which hierarchy elements are relocated, split or joined. The relations between hierarchy elements are visualized using Hierarchical Edge Bundles (HEBs). HEBs reduce visual clutter, they visually emphasize the aforementioned splits, joins, and relocations of subhierarchies, and they provide an intuitive way in which users can interact with the relations. The focus throughout this paper is on the comparison of different versions of hierarchically organized software systems, but the technique is applicable to other kinds of hierarchical data as well. Various data sets of actual software systems are used to show how our technique can be employed to easily spot splits, joins, and relocations of elements, how sorting both hierarchies with respect to each other facilitates comparison tasks, and how user interaction is supported.

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Parallel coordinate plots (PCPs) are a well-known visualization technique for viewing multivariate data. In the past, various visual modifications to PCPs have been proposed to facilitate tasks such as correlation and cluster identification, to reduce visual clutter, and to increase their information throughput. Most modifications pertain to the use of color and opacity, smooth curves, or the use of animation. Although many of these seem valid improvements, only few user studies have been performed to investigate this, especially with respect to cluster identification. We performed a user study to evaluate cluster identification performance -with respect to response time and correctness -of nine PCP variations, including standard PCPs. To generate the variations, we focused on covering existing techniques as well as possible while keeping testing feasible. This was done by adapting and merging techniques, which led to the following novel variations. The first is an effective way of embedding scatter plots into PCPs. The second is a technique for highlighting fuzzy clusters based on neighborhood density. The third is a spline-based drawing technique to reduce ambiguity. The last is a pair of animation schemes for PCP rotation. We present an overview of the tested PCP variations and the results of our study. The most important result is that a fair number of the seemingly valid improvements, with the exception of scatter plots embedded into PCPs, do not result in significant performance gains.