This is a survey on graph visualization and navigation techniques, as used in information visualization. Graphs appear in numerous applications such as Web browsing, state-transition diagrams, and data structures. The ability to visualize and to navigate in these potentially large, abstract graphs is often a crucial part of an application. Information visualization has specific requirements, which means that this survey approaches the results of traditional graph drawing from a different perspective.

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Graph visualization and navigation in information visualization: A survey

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

Hierarchical Edge Bundles: Visualization of Adjacency Relations in Hierarchical Data

Note: Professor Pach's number: [045]; Also in: Facsimile edition: World Classics in Mathematics Series, vol. 28, China Science Press, Beijing, 2006. Mimeographed from 100 Research Problems in Discrete Geometry (with W. O. J. Moser). Reference DCG-BOOK-2008-001 URL: http://www.math.nyu.edu/~pach/research_problems.html Record created on 2008-11-18, modified on 2017-05-12

Research Problems in Discrete Geometry

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.

Force-directed edge bundling for graph visualization

We present a model for building, visualizing, and interacting with multiscale representations of information visualization techniques using hierarchical aggregation. The motivation for this work is to make visual representations more visually scalable and less cluttered. The model allows for augmenting existing techniques with multiscale functionality, as well as for designing new visualization and interaction techniques that conform to this new class of visual representations. We give some examples of how to use the model for standard information visualization techniques such as scatterplots, parallel coordinates, and node-link diagrams, and discuss existing techniques that are based on hierarchical aggregation. This yields a set of design guidelines for aggregated visualizations. We also present a basic vocabulary of interaction techniques suitable for navigating these multiscale visualizations.

https://hal.inria.fr/hal-00696751/document

Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines

Clustered graphs are graphs with recursive clustering structures over the vertices. This type of structure appears in many systems. Examples include CASE tools, management information systems, VLSI design tools, and reverse engineering systems. Existing layout algorithms represent the clustering structure as recursively nested regions in the plane. However, as the structure becomes more and more complex, two dimensional plane representations tend to be insufficient. In this paper, firstly, we describe some two dimensional plane drawing algorithms for clustered graphs; then we show how to extend two dimensional plane drawings to three dimensional multilevel drawings. We consider two conventions: straight-line convex drawings and orthogonal rectangular drawings; and we show some examples.

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Multilevel Visualization of Clustered Graphs

In this paper, we introduce a new graph model known as clustered graphs, i.e. graphs with recursive clustering structures. This graph model has many applications in informational and mathematical sciences. In particular, we study C-planarity of clustered graphs. Given a clustered graph, the C-planarity testing problem is to determine whether the clustered graph can be drawn without edge crossings, or edge-region crossings. In this paper, we present efficient algorithms for testing C-planarity and finding C-planar embeddings of clustered graphs.

Planarity for Clustered Graphs

Hierarchical graphs and clustered graphs are useful nonclassical graph models for structured relational information Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures Both have applications in CASE tools, software visualization, VLSI design, etc Drawing algorithms for hierarchical graphs have been well investigated However, the problem of straight-line representation has not been addressed In this paper, we answer the question: does every planar hierarchical graph admit a planar straight-line hierarchical drawing? We present an algorithm that constructs such drawings in O(n2) time Also, we answer a basic question for clustered graphs, ie does every planar clustered graph admit a planar straight-line drawing with clusters drawn as convex polygons? A method for such drawings is provided in this paper

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Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

In this paper, we introduce and show how to draw a practical graph structure known as clustered graphs. We present an algorithm which produces planar, straight-line, convex drawings of clustered graphs in O(n2.5) time. We also demonstrate an area lower bound and an angle upper bound for straight-line convex drawings of C-planar graphs. We show that such drawings require Ω(2n) area and the smallest angle is O(1/n). Our bounds are unlike the area and angle bounds of classical graph drawing conventions in which area bound is Ω(n2) and angle bounds are functions of the maximum degree of the graph. Our results indicate important tradeoff between line straightness and area, and between region convexity and area.

How to Draw a Planar Clustered Graph

Hierarchical graphs and clustered graphs are useful non-classical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualization and VLSI design. Drawing algorithms for hierarchical graphs have been well investigated. However, the problem of planar straight-line representation has not been solved completely. In this paper we answer the question: does every planar hierarchical graph admit a planar straight-line hierarchical drawing? We present an algorithm that constructs such drawings in linear time. Also, we answer a basic question for clustered graphs, that is, does every planar clustered graph admit a planar straight-line drawing with clusters drawn as convex polygons? We provide a method for such drawings based on our algorithm for hierarchical graphs.

Qing-Wen Feng

Papers

Multilevel Visualization of Clustered Graphs

Planarity for Clustered Graphs

Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

How to Draw a Planar Clustered Graph

Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs