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23
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 139 (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.
Moiregraphs: Radial focus+context visualization and interaction for graphs with visual nodes
 in Proc. IEEE Symposium on Information Visualization, INFOVIS 2003, T. Munzner and
"... Graph and tree visualization techniques enable interactive exploration of complex relations while communicating topology. However, most existing techniques have not been designed for situations where visual information such as images is also present at each node and must be displayed. This paper pre ..."
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Cited by 31 (3 self)
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Graph and tree visualization techniques enable interactive exploration of complex relations while communicating topology. However, most existing techniques have not been designed for situations where visual information such as images is also present at each node and must be displayed. This paper presents MoireGraphs to address this need. MoireGraphs combine a new focus+context radial graph layout with a suite of interaction techniques (focus strength changing, radial rotation, level highlighting, secondary foci, animated transitions and node information) to assist in the exploration of graphs with visual nodes. The method is scalable to hundreds of displayed visual nodes.
Graphviz and dynagraph – static and dynamic graph drawing tools
 GRAPH DRAWING SOFTWARE
, 2003
"... Graphviz is a collection of software for viewing and manipulating abstract graphs. It provides graph visualization for tools and web sites in domains such as software engineering, networking, databases, knowledge representation, and bioinformatics. Hundreds of thousands of copies have been distribu ..."
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Cited by 25 (0 self)
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Graphviz is a collection of software for viewing and manipulating abstract graphs. It provides graph visualization for tools and web sites in domains such as software engineering, networking, databases, knowledge representation, and bioinformatics. Hundreds of thousands of copies have been distributed under an open source license. The core of Graphviz consists of implementations of various common types of graph layout. These layouts can be used via a C library interface, streambased command line tools, graphical user interfaces and web browsers. Aspects which distinguish the software include a retention of streambased interfaces in conjunction with a variety of tools for graph manipulation, and support for a wide assortment of graphical features and output formats. The former makes it possible to write highlevel programs for querying, modifying and displaying graphs. The latter allows Graphviz to be useful in a wide range of areas, with applications far removed from academic exercises. The algorithms of Graphviz concentrate on static layouts. Dynagraph is a sibling of Graphviz, with algorithms and interactive programs for incremental layout. At the library level, it provides an objectoriented interface for graphs and graph algorithms.
A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information
, 2007
"... In radial drawings of hierarchical graphs the vertices are placed on concentric circles rather than on horizontal lines and the edges are drawn as outwards monotone segments of spirals rather than straight lines as it is both done in the standard Sugiyama framework. This drawing style is well suite ..."
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Cited by 19 (7 self)
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In radial drawings of hierarchical graphs the vertices are placed on concentric circles rather than on horizontal lines and the edges are drawn as outwards monotone segments of spirals rather than straight lines as it is both done in the standard Sugiyama framework. This drawing style is well suited for the visualisation of centrality in social networks and similar concepts. Radial drawings also allow a more flexible edge routing than horizontal drawings, as edges can be routed around the center in two directions. In experimental results this reduces the number of crossings by approximately 30 percent on average. Few crossings are one of the major criteria for human readability. This paper is a detailed description of a complete framework for visualizing hierarchical information in a new radial fashion. Particularly, we briefly cover extensions of the level assignment step to benefit by the increasing perimeters of the circles, present three heuristics for crossing reduction in radial level drawings, and also show how to visualize the results.
Quantifying the SpaceEfficiency of 2D Graphical Representations of Trees
"... Abstract — A mathematical evaluation and comparison of the spaceefficiency of various 2D graphical representations of tree structures is presented. As part of the evaluation, a novel metric called the mean area exponent is introduced that quantifies the distribution of area across nodes in a tree r ..."
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Cited by 6 (1 self)
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Abstract — A mathematical evaluation and comparison of the spaceefficiency of various 2D graphical representations of tree structures is presented. As part of the evaluation, a novel metric called the mean area exponent is introduced that quantifies the distribution of area across nodes in a tree representation, and that can be applied to a broad range of different representations of trees. Several representations are analyzed and compared by calculating their mean area exponent as well as the area they allocate to nodes and labels. Our analysis inspires a set of design guidelines as well as a few novel tree representations that are also presented. Index Terms—Tree visualization, graph drawing, efficiency metrics. 1
Area Requirement of Gabriel Drawings
, 1996
"... In this paper we investigate the area requirement of proximity drawings and we prove an exponential lower bound. Namely, our main contribution is to show the existence of a class of Gabrieldrawable graphs that require exponential area for any Gabriel drawing and any resolution rule. Also, we extend ..."
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Cited by 5 (4 self)
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In this paper we investigate the area requirement of proximity drawings and we prove an exponential lower bound. Namely, our main contribution is to show the existence of a class of Gabrieldrawable graphs that require exponential area for any Gabriel drawing and any resolution rule. Also, we extend the result to an infinite class of proximity drawings.
D.: Indented pixel tree plots
 In: Proceedings of International Symposium on Visual Computing
, 2010
"... Abstract. We introduce Indented Pixel Tree Plots (IPTPs): a novel pixelbased visualization technique for depicting large hierarchies. It is inspired by the visual metaphor of indented outlines, omnipresent in graphical file browsers and pretty printing of source code. Inner vertices are represented ..."
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Cited by 3 (3 self)
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Abstract. We introduce Indented Pixel Tree Plots (IPTPs): a novel pixelbased visualization technique for depicting large hierarchies. It is inspired by the visual metaphor of indented outlines, omnipresent in graphical file browsers and pretty printing of source code. Inner vertices are represented as vertically arranged lines and leaf groups as horizontally arranged lines. A recursive layout algorithm places parent nodes to the left side of their underlying tree structure and leaves of each subtree grouped to the rightmost position. Edges are represented only implicitly by the vertically and horizontally aligned structure of the plot, leading to a sparse and redundantfree visual representation. We conducted a user study with 30 subjects in that we compared IPTPs and nodelink diagrams as a withinsubjects variable. The study indicates that working with IPTPs can be learned in less than 10 minutes. Moreover, IPTPs are as effective as nodelink diagrams for accuracy and completion time for three typical tasks; participants generally preferred IPTPs. We demonstrate the usefulness of IPTPs by understanding hierarchical features of huge trees such as the NCBI taxonomy with more than 300,000 nodes. 1
Adocs : a Drawing System for Generic Combinatorial Structures
, 1995
"... Existing graph drawing systems imply the use of specific algorithms for each kind of data structures. This paper provide a description of the Adocs program. The program is based on a generic description of the structures, and thus allows to draw structures of an infinite number of classes. It can be ..."
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Cited by 2 (0 self)
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Existing graph drawing systems imply the use of specific algorithms for each kind of data structures. This paper provide a description of the Adocs program. The program is based on a generic description of the structures, and thus allows to draw structures of an infinite number of classes. It can be used in order to produce graphical output for Gaffa, an uniform random generator of combinatorial structures. It could be used with other programs and is well suited for drawing compound objects.
Where to Draw the Line
, 1996
"... Graph Drawing (also known as Graph Visualization) tackles the problem of representing graphs on a visual medium such as computer screen, printer etc. Many applications such as software engineering, data base design, project planning, VLSI design, multimedia etc., have data structures that can be rep ..."
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Cited by 2 (0 self)
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Graph Drawing (also known as Graph Visualization) tackles the problem of representing graphs on a visual medium such as computer screen, printer etc. Many applications such as software engineering, data base design, project planning, VLSI design, multimedia etc., have data structures that can be represented as graphs. With the ever increasing complexity of these and new applications, and availability of hardware supporting visualization, the area of graph drawing is increasingly getting more attention from both practitioners and researchers. In a typical drawing of a graph, the vertices are represented as symbols such as circles, dots or boxes, etc., and the edges are drawn as continuous curves joining their end points. Often, the edges are simply drawn as (straight or poly) lines joining their end points (and hence the title of this thesis), followed by an optional transformation into smooth curves. The goal of research in graph drawing is to develop techniques for constructing good...
Computing and drawing isomorphic subgraphs
 Journal of Graph Algorithms and Applications
"... The isomorphic subgraph problem is finding two disjoint subgraphs of a graph which coincide on at least k edges. The graph is partitioned into a subgraph, its copy, and a remainder. The problem resembles the NPhard largest common subgraph problem, which searches copies of a graph in a pair of graph ..."
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Cited by 2 (0 self)
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The isomorphic subgraph problem is finding two disjoint subgraphs of a graph which coincide on at least k edges. The graph is partitioned into a subgraph, its copy, and a remainder. The problem resembles the NPhard largest common subgraph problem, which searches copies of a graph in a pair of graphs. In this paper we show that the isomorphic subgraph problem is NPhard, even for restricted instances such as connected outerplanar graphs. Then we present two different heuristics for the computation of maximal connected isomorphic subgraphs. Both heuristics use weighting functions and have been tested on four independent test suites. Finally, we introduce a spring algorithm which preserves isomorphic subgraphs and displays them as copies of each other. The drawing algorithm yields nice drawings and emphasizes the isomorphic subgraphs.