Peacock Bundles: Bundle Coloring for Graphs with Globality-Locality Trade-off

Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual edges. We propose a solution: we optimize edge coloring to differentiate bundled edges. We quantify strength of bundling in a flexible pairwise fashion between edges, and among bundled edges, we quantify how dissimilar their colors should be by dissimilarity of their origins and destinations. We solve the resulting nonlinear optimization, which is also interpretable as a novel dimensionality reduction task. In large graphs the necessary compromise is whether to differentiate colors sharply between locally occurring strongly bundled edges ("local bundles"), or also between the weakly bundled edges occurring globally over the graph ("global bundles"); we allow a user-set global-local tradeoff. We call the technique "peacock bundles". Experiments show the coloring clearly enhances comprehensibility of graph layouts with edge bundling.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

A Coloring Algorithm for Disambiguating Graph and Map Drawings

Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down eye movements. In this paper we propose an algorithm that disambiguates the edges with automatic selection of distinctive colors. Our proposed algorithm computes a near optimal color assignment of a dual collision graph, using a novel branch-and-bound procedure applied to a space decomposition of the color gamut. We give examples demonstrating the effectiveness of this approach in clarifying drawings of real world graphs and maps

Visualization of graphs and trees for software analysis

A software architecture is an abstraction of a software system, which is indispensable for many software engineering tasks. Unfortunately, in many cases information pertaining to the software architecture is not available, outdated, or inappropriate for the task at hand. The RECONSTRUCTOR project focuses on software architecture reconstruction, i.e., obtaining architectural information from an existing system. Our research, which is part of RECONSTRUCTOR, focuses on interactive visualization and tries to answer the following question: How can users be enabled to understand the large amounts of information relevant for program understanding using visual representations? To answer this question, we have iteratively developed a number of techniques for visualizing software systems. A large number of these cases consists of hierarchically organized data, combined with adjacency relations. Examples are function calls within a hierarchically organized software system and correspondence relations between two different versions of a hierarchically organized software system. Hierarchical Edge Bundles (HEBs) are used to visualize adjacency relations in hierarchically organized data, such as the aforementioned function calls within a software system. HEBs significantly reduce visual clutter by visually bundling relations together. Massive Sequence Views (MSVs) are used in conjunction with HEBs to enable analysis of sequences of relations, such as function-call traces. HEBs are furthermore used to visually compare hierarchically organized data, e.g., two different versions of a software system. HEBs visually emphasize splits, joins, and relocations of subhierarchies and provide for interactive selection of sets of relations. Since HEBs require a hierarchy to perform the bundling, we present Force-Directed Edge Bundles (FDEBs) as an alternative to visually bundle relations together in the absence of a hierarchical component. FDEBs use a self-organizing approach to bundling in which edges are modeled as flexible springs that can attract each other. As a result, visual clutter is reduced and high-level edge patterns are better visible. Finally, in all these methods, a clear depiction of the direction of edges is important. We have therefore performed a separate study in which we evaluated ten representations (including the standard arrow) for depicting directed edges in a controlled user study

DEPLOYING, IMPROVING AND EVALUATING EDGE BUNDLING METHODS FOR VISUALIZING LARGE GRAPHS

A tremendous increase in the scale of graphs has been witnessed in a wide range of fields, which demands efficient and effective visualization techniques to assist users in better understandings of large graphs. Conventional node-link diagrams are often used to visualize graphs, whereas excessive edge crossings can easily incur severe visual clutter in the node-link diagram of a large graph. Edge bundling can effectively remedy visual clutter and reveal high-level graph structures. Although significant efforts have been devoted to developing edge bundling, three challenging problems remain. First, edge bundling techniques are often computationally expensive and are not easy to deploy for web-based applications. The state-of-the-art edge bundling methods often require special system supports and techniques such as high-end GPU acceleration for large graphs, which makes these methods less portable, especially for ubiquitous mobile devices. Second, the quantitative quality of edge bundling results is barely assessed in the literature. Currently, the comparison of edge bundling mainly focuses on computational performance and perceptual results. Third, although the family of edge bundling techniques has a rich set of bundling layout, there is a lack of a generic method to generate different styles of edge bundling. In this research, I aim to address these problems and have made the following contributions. First, I provide an efficient framework to deploy edge bundling for web-based platforms by exploiting standard graphics hardware functions and libraries. My framework can generate high-quality edge bundling results on web-based platforms, and achieve a speedup of 50X compared to the previous state-of-the-art edge bundling method on a graph with half of a million edges. Second, I propose a new moving least squares based approach to lower the algorithm complexity of edge bundling. In addition, my approach can generate better bundling results compared to other methods based on a quality metric. Third, I provide an information-theoretic metric to evaluate the edge bundling methods. I leverage information theory in this metric. With my information-theoretic metric, domain users can choose appropriate edge bundling methods with proper parameters for their applications. Last but not least, I present a deep learning framework for edge bundling visualizations. Through a training process that learns the results of a specific edge bundling method, my deep learning framework can infer the final layout of the edge bundling method. My deep learning framework is a generic framework that can generate the corresponding results of different edge bundling methods. Adviser: Hongfeng Y

Visualizing and Interacting with Geospatial Networks:A Survey and Design Space

This paper surveys visualization and interaction techniques for geospatial networks from a total of 95 papers. Geospatial networks are graphs where nodes and links can be associated with geographic locations. Examples can include social networks, trade and migration, as well as traffic and transport networks. Visualizing geospatial networks poses numerous challenges around the integration of both network and geographical information as well as additional information such as node and link attributes, time, and uncertainty. Our overview analyzes existing techniques along four dimensions: i) the representation of geographical information, ii) the representation of network information, iii) the visual integration of both, and iv) the use of interaction. These four dimensions allow us to discuss techniques with respect to the trade-offs they make between showing information across all these dimensions and how they solve the problem of showing as much information as necessary while maintaining readability of the visualization. https://geonetworks.github.io.Comment: To be published in the Computer Graphics Forum (CGF) journa

An Information-Theoretic Framework for Evaluating Edge Bundling Visualization

Edge bundling is a promising graph visualization approach to simplifying the visual result of a graph drawing. Plenty of edge bundling methods have been developed to generate diverse graph layouts. However, it is difficult to defend an edge bundling method with its resulting layout against other edge bundling methods as a clear theoretic evaluation framework is absent in the literature. In this paper, we propose an information-theoretic framework to evaluate the visual results of edge bundling techniques. We first illustrate the advantage of edge bundling visualizations for large graphs, and pinpoint the ambiguity resulting from drawing results. Second, we define and quantify the amount of information delivered by edge bundling visualization from the underlying network using information theory. Third, we propose a new algorithm to evaluate the resulting layouts of edge bundling using the amount of the mutual information between a raw network dataset and its edge bundling visualization. Comparison examples based on the proposed framework between different edge bundling techniques are presented

Scalability considerations for multivariate graph visualization

Real-world, multivariate datasets are frequently too large to show in their entirety on a visual display. Still, there are many techniques we can employ to show useful partial views-sufficient to support incremental exploration of large graph datasets. In this chapter, we first explore the cognitive and architectural limitations which restrict the amount of visual bandwidth available to multivariate graph visualization approaches. These limitations afford several design approaches, which we systematically explore. Finally, we survey systems and studies that exhibit these design strategies to mitigate these perceptual and architectural limitations