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68
Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data
 IEEE Transactions on Visualization and Computer Graphics
, 2006
"... Abstract—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., nonhierarch ..."
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Cited by 144 (9 self)
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Abstract—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., nonhierarchical 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 Bspline 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.
View management for virtual and augmented reality
, 2001
"... We describe a viewmanagement component for interactive 3D user interfaces. By view management, we mean maintaining visual constraints on the projections of objects on the view plane, such as locating related objects near each other, or preventing objects from occluding each other. Our viewmanageme ..."
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Cited by 86 (18 self)
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We describe a viewmanagement component for interactive 3D user interfaces. By view management, we mean maintaining visual constraints on the projections of objects on the view plane, such as locating related objects near each other, or preventing objects from occluding each other. Our viewmanagement component accomplishes this by modifying selected object properties, including position, size, and transparency, which are tagged to indicate their constraints. For example, some objects may have geometric properties that are determined entirely by a physical simulation and which cannot be modified, while other objects may be annotations whose position and size are flexible. We introduce algorithms that use upright rectangular extents to represent on the view plane a dynamic and efficient approximation of the occupied space containing the projections of visible portions of 3D objects, as well as the unoccupied space in which objects can be placed to
MatrixExplorer: a DualRepresentation System to Explore Social Networks
 IEEE Transactions on Visualization and Computer Graphics
, 2006
"... Abstract — MatrixExplorer is a network visualization system that uses two representations: nodelink diagrams and matrices. Its design comes from a list of requirements formalized after several interviews and a participatory design session conducted with social science researchers. Although matrices ..."
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Cited by 55 (11 self)
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Abstract — MatrixExplorer is a network visualization system that uses two representations: nodelink diagrams and matrices. Its design comes from a list of requirements formalized after several interviews and a participatory design session conducted with social science researchers. Although matrices are commonly used in social networks analysis, very few systems support the matrixbased representations to visualize and analyze networks. MatrixExplorer provides several novel features to support the exploration of social networks with a matrixbased representation, in addition to the standard interactive filtering and clustering functions. It provides tools to reorder (layout) matrices, to annotate and compare findings across different layouts and find consensus among several clusterings. MatrixExplorer also supports Nodelink diagram views which are familiar to most users and remain a convenient way to publish or communicate exploration results. Matrix and nodelink representations are kept synchronized at all stages of the exploration process. Index Terms — social networks visualization, nodelink diagrams, matrixbased representations, exploratory process, matrix ordering, interactive clustering, consensus. Fig. 1. MatrixExplorer showing two synchronized representations of the same network: matrix on the left and nodelink on the right. 1
Navigating clustered graphs using forcedirected methods
 Journal of Graph Algorithms and Applications
, 2000
"... Graphs which arise in Information Visualization applications are typically very large: thousands, or perhaps millions of nodes. Current graph drawing methods successfully deal with (at best) a few hundred nodes. This paper describes a strategy for the visualization and navigation of graphs. The stra ..."
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Cited by 46 (1 self)
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Graphs which arise in Information Visualization applications are typically very large: thousands, or perhaps millions of nodes. Current graph drawing methods successfully deal with (at best) a few hundred nodes. This paper describes a strategy for the visualization and navigation of graphs. The strategy has three elements: 1. A layered architecture, called CGA, for handling clustered graphs: these are graphs with a hierarchical node clustering superimposed. 2. An online forcedirected graph drawing method. 3. Animation methods. Using this strategy, a user may view an abridgment of a graph, that is, a small part of the graph that is currently of interest. By changing the abridgment, the user may travel through the graph. The changes use animation to smoothly transform one view to the next. The strategy has been implemented in a prototype system called DATU. Communicated by G. Liotta and S. H. Whitesides: submitted September 1998; revised
Drawing areaproportional Venn and Euler diagrams
 In Proceedings of Graph Drawing 2003
, 2003
"... Abstract. We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These areaproportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey informatio ..."
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Cited by 46 (1 self)
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Abstract. We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These areaproportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey information about data sets with interacting characteristics. We develop algorithms for drawing areaproportional Venn diagrams for any population distribution over two characteristics using circles and over three characteristics using rectangles and nearrectangular polygons; modifications of these algorithms are then presented for drawing the more general Euler diagrams. We present results concerning which population distributions can be drawn using specific shapes. A program to aid further investigation of areaproportional Venn diagrams is also described. 1
Clustering Software Artifacts Based on Frequent Common Changes
 In Proc. IWPC
, 2005
"... Changes of software systems are less expensive and less errorprone if they affect only one subsystem. Thus, clusters of artifacts that are frequently changed together are subsystem candidates. We introduce a twostep method for identifying such clusters. First, a model of common changes of software ..."
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Cited by 43 (9 self)
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Changes of software systems are less expensive and less errorprone if they affect only one subsystem. Thus, clusters of artifacts that are frequently changed together are subsystem candidates. We introduce a twostep method for identifying such clusters. First, a model of common changes of software artifacts, called cochange graph, is extracted from the version control repository of the software system. Second, a layout of the cochange graph is computed that reveals clusters of frequently cochanged artifacts. We derive requirements for such layouts, and introduce an energy model for producing layouts that fulfill these requirements. We evaluate the method by applying it to three example systems, and comparing the resulting layouts to authoritative decompositions.
VisLink: revealing relationships amongst visualizations
 IEEE TRANS VIS COMPUT GRAPH
, 2007
"... We present VisLink, a method by which visualizations and the relationships between them can be interactively explored. VisLink readily generalizes to support multiple visualizations, empowers interrepresentational queries, and enables the reuse of the spatial variables, thus supporting efficient i ..."
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Cited by 42 (5 self)
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We present VisLink, a method by which visualizations and the relationships between them can be interactively explored. VisLink readily generalizes to support multiple visualizations, empowers interrepresentational queries, and enables the reuse of the spatial variables, thus supporting efficient information encoding and providing for powerful visualization bridging. Our approach uses multiple 2D layouts, drawing each one in its own plane. These planes can then be placed and repositioned in 3D space: side by side, in parallel, or in chosen placements that provide favoured views. Relationships, connections, and patterns between visualizations can be revealed and explored using a variety of interaction techniques including spreading activation and search filters.
An Energy Model for Visual Graph Clustering
 Proceedings of the 11th International Symposium on Graph Drawing (GD 2003), LNCS 2912
, 2003
"... We introduce an energy model whose minimum energy drawings reveal the clusters of the drawn graph. Here a cluster is a set of nodes with many internal edges and few edges to nodes outside the set. The drawings of the bestknown force and energy models do not clearly show clusters for graphs whose ..."
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Cited by 41 (4 self)
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We introduce an energy model whose minimum energy drawings reveal the clusters of the drawn graph. Here a cluster is a set of nodes with many internal edges and few edges to nodes outside the set. The drawings of the bestknown force and energy models do not clearly show clusters for graphs whose diameter is small relative to the number of nodes. We formally characterize the minimum energy drawings of our energy model. This characterization shows in what sense the drawings separate clusters, and how the distance of separated clusters to the other nodes can be interpreted.
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 37 (0 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.
Efficient Aggregation for Graph Summarization
"... Graphs are widely used to model real world objects and their relationships, and large graph datasets are common in many application domains. To understand the underlying characteristics of large graphs, graph summarization techniques are critical. However, existing graph summarization methods are mo ..."
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Cited by 34 (3 self)
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Graphs are widely used to model real world objects and their relationships, and large graph datasets are common in many application domains. To understand the underlying characteristics of large graphs, graph summarization techniques are critical. However, existing graph summarization methods are mostly statistical (studying statistics such as degree distributions, hopplots and clustering coefficients). These statistical methods are very useful, but the resolutions of the summaries are hard to control. In this paper, we introduce two databasestyle operations to summarize graphs. Like the OLAPstyle aggregation methods that allow users to drilldown or rollup to control the resolution of summarization, our methods provide an analogous functionality for large graph datasets. The first operation, called SNAP, produces a summary graph by grouping nodes based on userselected node attributes and relationships. The second operation, called kSNAP, further allows users to control the resolutions of summaries and provides the “drilldown ” and “rollup ” abilities to navigate through summaries with different resolutions. We propose an efficient algorithm to evaluate the SNAP operation. In addition, we prove that the kSNAP computation is NPcomplete. We propose two heuristic methods to approximate the kSNAP results. Through extensive experiments on a variety of real and synthetic datasets, we demonstrate the effectiveness and efficiency of the proposed methods.