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17
ForceDirected Edge Bundling for Graph Visualization
, 2009
"... Graphs depicted as nodelink 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 highlevel edge patterns. Previous methods requ ..."
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Cited by 81 (1 self)
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Graphs depicted as nodelink 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 highlevel 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 selforganizing 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 highlevel 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.
IPSepCoLa: An incremental procedure for separation constraint layout of graphs
 IEEE Trans. Visualization and Computer Graphics
, 2006
"... Abstract—We extend the popular forcedirected approach to network (or graph) layout to allow separation constraints, which enforce a minimum horizontal or vertical separation between selected pairs of nodes. This simple class of linear constraints is expressive enough to satisfy a wide variety of ap ..."
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Cited by 44 (19 self)
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Abstract—We extend the popular forcedirected approach to network (or graph) layout to allow separation constraints, which enforce a minimum horizontal or vertical separation between selected pairs of nodes. This simple class of linear constraints is expressive enough to satisfy a wide variety of applicationspecific layout requirements, including: layout of directed graphs to better show flow; layout with nonoverlapping node labels; and layout of graphs with grouped nodes (called clusters). In the stress majorization forcedirected layout process, separation constraints can be treated as a quadratic programming problem. We give an incremental algorithm based on gradient projection for efficiently solving this problem. The algorithm is considerably faster than using generic constraint optimization techniques and is comparable in speed to unconstrained stress majorization. We demonstrate the utility of our technique with sample data from a number of practical applications including geneactivation networks, terrorist networks and visualization of highdimensional data. Index Terms—Graph drawing, constraints, stress majorization, force directed algorithms,multidimensional scaling. F Many fields of science, technology and industry require visualization of networks. For example, biologists study geneactivation networks and metabolic pathways, police study networks of associations between suspects to uncover organized crime or terrorist cells, and
Skeletonbased edge bundling for graph visualization
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, 2011, 17 (12), PP 23642373
, 2011
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Topology Preserving Constrained Graph Layout
, 2008
"... Constrained graph layout is a recent generalisation of forcedirected graph layout which allows constraints on node placement. We give a constrained graph layout algorithm that takes an initial feasible layout and improves it while preserving the topology of the initial layout. The algorithm suppo ..."
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Cited by 15 (7 self)
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Constrained graph layout is a recent generalisation of forcedirected graph layout which allows constraints on node placement. We give a constrained graph layout algorithm that takes an initial feasible layout and improves it while preserving the topology of the initial layout. The algorithm supports polyline connectors and clusters. During layout the connectors and cluster boundaries act like impervious rubberbands which try to shrink in length. The intended application for our algorithm is dynamic graph layout, but it can also be used to improve layouts generated by other graph layout techniques.
Smooth Bundling of Large Streaming and Sequence Graphs
, 2013
"... Dynamic graphs are increasingly pervasive in modern information systems. However, understanding how a graph changes in time is difficult. We present here two techniques for simplified visualization of dynamic graphs using edge bundles. The first technique uses a recent imagebased graph bundling met ..."
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Cited by 8 (5 self)
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Dynamic graphs are increasingly pervasive in modern information systems. However, understanding how a graph changes in time is difficult. We present here two techniques for simplified visualization of dynamic graphs using edge bundles. The first technique uses a recent imagebased graph bundling method to create smoothly changing bundles from streaming graphs. The second technique incorporates additional edgecorrespondence data and is thereby suited to visualize discrete graph sequences. We illustrate our methods with examples from realworld large dynamic graph datasets.
Bundled Visualization of Dynamic Graph and Trail Data
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2013
"... Depicting change captured by dynamic graphs and temporal paths, or trails, is hard. We present two techniques for simplified visualization of such datasets using edge bundles. The first technique uses an efficient imagebased bundling method to create smoothly changing bundles from streaming graph ..."
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Cited by 6 (2 self)
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Depicting change captured by dynamic graphs and temporal paths, or trails, is hard. We present two techniques for simplified visualization of such datasets using edge bundles. The first technique uses an efficient imagebased bundling method to create smoothly changing bundles from streaming graphs. The second technique adds edgecorrespondence data atop of any static bundling algorithm, and is best suited for graph sequences. We show how these techniques can produce simplified visualizations of streaming and sequence graphs. Next, we show how several temporal attributes can be added atop of our dynamic graphs. We illustrate our techniques with datasets from aircraft monitoring, software engineering, and eyetracking of static and dynamic scenes.
Constrained stress majorization using diagonally scaled gradient projection
, 2007
"... Constrained stress majorization is a promising new technique for integrating application specific layout constraints into forcedirected graph layout. We significantly improve the speed and convergence properties of the constrained stressmajorization technique for graph layout by employing a diagon ..."
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Cited by 5 (3 self)
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Constrained stress majorization is a promising new technique for integrating application specific layout constraints into forcedirected graph layout. We significantly improve the speed and convergence properties of the constrained stressmajorization technique for graph layout by employing a diagonal scaling of the stress function. Diagonal scaling requires the activeset quadratic programming solver used in the projection step to be extended to handle separation constraints with scaled variables, i.e. of the form siyi + gij ≤ sjyj. The changes, although relatively small, are quite subtle and explained in detail.
Attributedriven edge bundling for general graphs with applications in trail analysis
 In Proc. IEEE PacificVis
, 2015
"... Edge bundling methods reduce visual clutter of dense and occluded graphs. However, existing bundling techniques either ignore edge properties such as direction and data attributes, or are otherwise computationally not scalable, which makes them unsuitable for tasks such as exploration of large traj ..."
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Cited by 2 (0 self)
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Edge bundling methods reduce visual clutter of dense and occluded graphs. However, existing bundling techniques either ignore edge properties such as direction and data attributes, or are otherwise computationally not scalable, which makes them unsuitable for tasks such as exploration of large trajectory datasets. We present a new framework to generate bundled graph layouts according to any numerical edge attributes such as directions, timestamps or weights. We propose a GPUbased implementation linear in number of edges, which makes our algorithm applicable to large datasets. We demonstrate our method with applications in the analysis of aircraft trajectory datasets and eyemovement traces.