This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each edge belongs to a group that may either be an input of the problem or found by clustering one or more edge properties such as origin, destination, orientation, length or domain-specific properties. Bundling is driven by a stack of density maps, with each map capturing both the edge density of a given group as well as interactions with edges from other groups. Density maps are efficiently calculated by smoothing 2D histograms of edge occurrence using repeated averaging filters based on integral images. A CPU implementation of the algorithm is tested on several graphs, and different grouping criteria are used to illustrate how the proposed technique can render different visualizations of the same data. Bundling performance is much higher than on previous approaches, being particularly noticeable on large graphs, with millions of edges being bundled in seconds.
Visualization of graphs containing many nodes and edges efficiently is quite challenging since representations generally suffer from visual clutter induced by the large amount of edge crossings and node-edge overlaps. That problem becomes even more important when nodes positions are fixed, such as in geography were nodes positions are set according to geographical coordinates. Edge bundling techniques can help to solve this issue by visually merging edges along common routes but it can also help to reveal high-level edge patterns in the network and therefore to understand its overall organization. In this paper, we present a generalization of [18] to reduce the clutter in a 3D representation by routing edges into bundles as well as a GPU-based rendering method to emphasize bundles densities while preserving edge color. To visualize geographical networks in the context of the globe, we also provide a new technique allowing to bundle edges around and not across it. 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. Visualizing graphs containing many nodes and edges efficiently is quite challenging. Drawings of such graphs generally suffer from visual clutter induced by the large amount of edges and their crossings. Consequently, it is difficult to read the relationships between nodes and the high-level edge patterns that may exist in standard nodelink diagram representations. Edge bundling techniques have been proposed to help solve this issue, which rely on high quality edge rerouting. In this paper, we introduce an intuitive edge bundling technique which efficiently reduces edge clutter in graphs drawings. Our method is based on the use of a grid built using the original graph to compute the edge rerouting. In comparison with previously proposed edge bundling methods, our technique improves both the level of clutter reduction and the computation performance. The second contribution of this paper is a GPU-based rendering method which helps users perceive bundles densities while preserving edge color. Graphs have been widely used to model relationships among data. For large graphs, excessive edge crossings make the display visually cluttered and thus difficult to explore. In this paper, we propose a novel geometry-based edge-clustering framework that can group edges into bundles to reduce the overall edge crossings. Our method uses a control mesh to guide the edge-clustering process; edge bundles can be formed by forcing all edges to pass through some control points on the mesh. The control mesh can be generated at different levels of detail either manually or automatically based on underlying graph patterns. Users can further interact with the edge-clustering results through several advanced visualization techniques such as color and opacity enhancement. Compared with other edge-clustering methods, our approach is intuitive, flexible, and efficient. The experiments on some large graphs demonstrate the effectiveness of our method. The node-link diagram is an intuitive and venerable way to depict a graph. To reduce clutter and improve the readability of node-link views, Holten & van Wijk's force-directed edge bundling employs a physical simulation to spatially group graph edges. While both useful and aesthetic, this technique has shortcomings: it bundles spatially proximal edges regardless of direction, weight, or graph connectivity. As a result, high-level directional edge patterns are obscured. We present divided edge bundling to tackle these shortcomings. By modifying the forces in the physical simulation, directional lanes appear as an emergent property of edge direction. By considering graph topology, we only bundle edges related by graph structure. Finally, we aggregate edge weights in bundles to enable more accurate visualization of total bundle weights. We compare visualizations created using our technique to standard force-directed edge bundling, matrix diagrams, and clustered graphs; we find that divided edge bundling leads to visualizations that are easier to interpret and reveal both familiar and previously obscured patterns.