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graph - Geometry-Based Edge Clustering for Graph...

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Geometry-Based Edge Clustering for Graph Visualization Weiwei Cui, Hong Zhou, Student Member, IEEE , Huamin Qu, Member, IEEE , Pak Chung Wong, and Xiaoming Li Abstract —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. Index Terms —Graph visualization, visual clutter, mesh, edge clustering 1 I NTRODUCTION Graphs have been widely used to model many problems such as cita- tions in scientific papers, traffic between telecommunication switches, and airline routes among cities. The scale of these problems keeps in- creasing and the associated graphs can easily contain tens of thousands of nodes and edges. Visual clutter caused by excessive edge crossings has made traditional layouts no longer effective to convey information. Thus, reducing visual clutter in graphs is a very important research problem. An informative and clear graph layout is critical for clutter reduction. Many methods have been proposed to improve graph layout. These methods can be classified into two major categories: adjust node po- sitions and improve edge layout. Rearranging the nodes can decrease edge crossings in graphs and thus reduce edge clutter. Node layout methods, such as force-based model algorithm [17], can generate vi- sually pleasing results for small or medium sized graphs according to some aesthetic criteria. However, for dense graphs with a substan- tial number of edges, rearranging the nodes usually cannot reduce the edge crossings to a satisfactory level. In addition, nodes in some ap- plications such as airline routes have semantic meanings and it may not be appropriate to move their positions. Another promising ap- proach to reduce visual clutter is to bundle edges. For example, a flow map layout [18] is proposed for single-source graphs while Edge Bun- dles [12] are designed for visualizing datasets containing both hier- archical structures and adjacency relations. Their results demonstrate the high potential of using edge clustering to improve the graph layout and reduce visual clutter. However, these previous solutions are all de- signed for special graphs such as source-sink style graphs and graphs with known hierarchical structures. An efficient edge-clustering solu-
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