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24
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.
Visual Clustering of Graphs with Nonuniform Degrees
 Proceedings of the 13th International Symposium on Graph Drawing (GD 2005
, 2004
"... We discuss several criteria for clustering graphs, and identify two criteria which are not biased towards certain cluster sizes: the nodenormalized cut (also called cut ratio) and the edgenormalized cut. We present two energy models whose minimum energy drawings reveal clusters with respect to ..."
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Cited by 27 (2 self)
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We discuss several criteria for clustering graphs, and identify two criteria which are not biased towards certain cluster sizes: the nodenormalized cut (also called cut ratio) and the edgenormalized cut. We present two energy models whose minimum energy drawings reveal clusters with respect to these criteria.
Simultaneous graph drawing: Layout algorithms and visualization schemes
 In 11th Symposium on Graph Drawing (GD
, 2003
"... Abstract. In this paper we consider the problem of drawing and displaying a series of related graphs, i.e., graphs that share all, or parts of the same vertex set. We designed and implemented three different algorithms for simultaneous graphs drawing and three different visualization schemes. The al ..."
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Cited by 21 (6 self)
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Abstract. In this paper we consider the problem of drawing and displaying a series of related graphs, i.e., graphs that share all, or parts of the same vertex set. We designed and implemented three different algorithms for simultaneous graphs drawing and three different visualization schemes. The algorithms are based on a modification of the forcedirected algorithm that allows us to take into account vertex weights and edge weights in order to achieve mental map preservation while obtaining individually readable drawings. The implementation is in Java and the system can be downloaded at
Local Multidimensional Scaling for Nonlinear Dimension Reduction, Graph Layout and Proximity Analysis
, 2006
"... In recent years there has been a resurgence of interest in nonlinear dimension reduction methods. Among new proposals are socalled “Local Linear Embedding ” (LLE) and “Isomap”. Both use local neighborhood information to construct a global lowdimensional embedding of a hypothetical manifold near w ..."
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Cited by 16 (3 self)
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In recent years there has been a resurgence of interest in nonlinear dimension reduction methods. Among new proposals are socalled “Local Linear Embedding ” (LLE) and “Isomap”. Both use local neighborhood information to construct a global lowdimensional embedding of a hypothetical manifold near which the data fall. In this paper we introduce a family of new nonlinear dimension reduction methods called “Local Multidimensional Scaling ” or LMDS. Like LLE and Isomap, LMDS only uses local information from userchosen neighborhoods, but it differs from them in that it uses ideas from the area of “graph layout”. A common paradigm in graph layout is to achieve desirable drawings of graphs by minimizing energy functions that balance attractive forces between near points and repulsive forces between nonnear points against each other. We approach the force paradigm by proposing a parametrized family of stress or energy functions inspired by BoxCox power transformations. This family provides users with considerable flexibility for achieving desirable embeddings, and it comprises most energy functions proposed in the past.
Graphs, they are changing  dynamic graph drawing for a sequence of graphs
 Proc. 10th Int. Symp. Graph Drawing (GD 2002), number 2528 in Lecture Notes in Computer Science, LNCS
, 2002
"... Abstract. In this paper we present a generic algorithm for drawing sequences of graphs. This algorithm works for different layout algorithms and related metrics and adjustment strategies. It differs from previous work on dynamic graph drawing in that it considers all graphs in the sequence (offline) ..."
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Cited by 15 (0 self)
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Abstract. In this paper we present a generic algorithm for drawing sequences of graphs. This algorithm works for different layout algorithms and related metrics and adjustment strategies. It differs from previous work on dynamic graph drawing in that it considers all graphs in the sequence (offline) instead of just the previous ones (online) when computing the layout for each graph of the sequence. We introduce several general adjustment strategies and give examples of these strategies in the context of forcedirected graph layout. Finally some results from our first prototype implementation are discussed. 1
A Space of Layout Styles for Hierarchical Graph Models of Software Systems
, 2005
"... Hierarchical graphs are widely used as models of the structure of software systems. A central problem in the visualization of hierarchical graphs is the computation of layouts, i.e. of positions of the nodes in two or threedimensional space. We derive requirements for graph layouts from various so ..."
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Cited by 12 (2 self)
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Hierarchical graphs are widely used as models of the structure of software systems. A central problem in the visualization of hierarchical graphs is the computation of layouts, i.e. of positions of the nodes in two or threedimensional space. We derive requirements for graph layouts from various software analysis questions, and classify the required layouts along three dimensions: layouts with meaningful distances between single nodes vs. layouts with meaningful distances between groups of nodes, layouts reflecting adjacency vs. layouts reflecting hierarchy, and layouts that faithfully reflect the size of subgraphs vs. layouts where certain subgraphs are magnified. We present a fairly simple and theoretically validated energy model for computing such layouts.
An Experimental Study on DistanceBased Graph Drawing (Extended Abstract)
, 2009
"... In numerous application areas, general undirected graphs need to be drawn, and forcedirected layout appears to be the most frequent choice. We present an extensive experimental study showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms base ..."
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Cited by 11 (5 self)
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In numerous application areas, general undirected graphs need to be drawn, and forcedirected layout appears to be the most frequent choice. We present an extensive experimental study showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms based on variants of multidimensional scaling is to be preferred because of their efficiency, reliability, and even simplicity. We also hope that details in the design of our study help advance experimental methodology in algorithm engineering and graph drawing, independent of the case at hand.
Mining CoChange Clusters from Version Repositories
, 2005
"... Clusters of software artifacts that are frequently changed together are subsystem candidates, because one of the main goals of software design is to make changes local. The contribution of this paper is a visualizationbased method that supports the identification of such clusters. First, we define ..."
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Cited by 9 (4 self)
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Clusters of software artifacts that are frequently changed together are subsystem candidates, because one of the main goals of software design is to make changes local. The contribution of this paper is a visualizationbased method that supports the identification of such clusters. First, we define the cochange graph as a simple but powerful model of common changes of software artifacts, and describe how to extract the graph from version control repositories. Second, we introduce an energy model for computing forcedirected layouts of cochange graphs. The resulting layouts have a welldefined interpretation in terms of the structure of the visualized graph, and clearly reveal groups of frequently cochanged artifacts. We evaluate our method by comparing the layouts for three example projects with authoritative subsystem decompositions.
Visualizing Biodiversity with Voronoi Treemaps
 In Proc. Sixth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD'09
, 2009
"... Abstract—Introduced in 2005, the Voronoi treemap algorithm is an information visualization technique for displaying hierarchical data. Voronoi treemaps use weighted, centroidal Voronoi diagrams to create a nested tessellation of convex polygons. However, despite appealing qualities, few real world e ..."
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Cited by 8 (1 self)
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Abstract—Introduced in 2005, the Voronoi treemap algorithm is an information visualization technique for displaying hierarchical data. Voronoi treemaps use weighted, centroidal Voronoi diagrams to create a nested tessellation of convex polygons. However, despite appealing qualities, few real world examples of Voronoi treemaps exist. In this paper, we present a multitouch tabletop application called Involv that uses the Voronoi treemap algorithm to create an interactive visualization for the Encyclopedia of Life. Involv is the result of a yearlong iterative development process and includes over 1.2 million named species organized in a ninelevel hierarchy. Working in the domain of life sciences, we have encountered the need to display supplemental hierarchical data to augment information in the treemap. Thus we propose an extension of the Voronoi treemap algorithm that employs forcedirected graph drawing techniques both to guide the construction of the treemap and to overlay a supplemental hierarchy. KeywordsVoronoi treemaps; information visualization; multitouch tabletop displays; interaction design; biodiversity I.
Dynamic Graph Drawing in Visone
, 2008
"... In early 2008 a new testing branch of the network analysis software visone has been made publicly available [Baur et al., 2008]. This realease includes the ability to process dynamic networks. A central feature is a dedicated dynamic layout algorithm which we present here from a methological and app ..."
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Cited by 7 (1 self)
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In early 2008 a new testing branch of the network analysis software visone has been made publicly available [Baur et al., 2008]. This realease includes the ability to process dynamic networks. A central feature is a dedicated dynamic layout algorithm which we present here from a methological and application oriented point of view. We first describe this algorithm from an algorithmic perspective. More precisely we show how the local majorant method of the related layout algorithm given by Kamada and Kawai can be adapted to layout dynamic networks. Following the methodological part we also address some problems and some other features of our implementation. Given the information in this document users of the dynamic layout procedure in visone should be able to employ the various available options efficiently to get the desired results. 1