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29
An Eye Tracking Study into the Effects of Graph Layout
, 2009
"... Graphs are typically visualized as nodelink diagrams. Although there is a fair amount of research focusing on crossing minimization to improve readability, little attention has been paid on how to handle crossings when they are an essential part of the final visualizations. This requires us to unde ..."
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Graphs are typically visualized as nodelink diagrams. Although there is a fair amount of research focusing on crossing minimization to improve readability, little attention has been paid on how to handle crossings when they are an essential part of the final visualizations. This requires us to understand how people read graphs and how crossings affect reading performance. As an initial step to this end, a preliminary eye tracking experiment was conducted. The specific purpose of this experiment was to test the effects of crossing angles and geometricpath tendency on eye movements and performance. Sixteen subjects performed both path search and node locating tasks with six drawings. The results showed that small angles can slow down and trigger extra eye movements, causing delays for path search tasks, whereas crossings have little impact on node locating tasks. Geometricpath tendency indicates that a path between two nodes can become harder to follow when many branches of the path go toward the target node. The insights obtained are discussed with a view to further confirmation in future work.
Cyclic Leveling of Directed Graphs
"... The Sugiyama framework is the most commonly used concept for visualizing directed graphs. It draws them in a hierarchical way and operates in four phases: cycle removal, leveling, crossing reduction, and coordinate assignment. However, there are situations where cycles must be displayed as such, e ..."
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The Sugiyama framework is the most commonly used concept for visualizing directed graphs. It draws them in a hierarchical way and operates in four phases: cycle removal, leveling, crossing reduction, and coordinate assignment. However, there are situations where cycles must be displayed as such, e.g., distinguished cycles in the biosciences and processes that repeat in a daily or weekly turn. This forbids the removal of cycles. In their seminal paper Sugiyama et al. also introduced recurrent hierarchies as a concept to draw graphs with cycles. However, this concept has not received much attention since then. In this paper we investigate the leveling problem for cyclic graphs. We show that minimizing the sum of the length of all edges is N Phard for a given number of levels and present three different heuristics for the leveling problem. This sharply contrasts the situation in the hierarchical style of drawing directed graphs, where this problem is solvable in polynomial time.
A Summary of
 the International Standard Date and Time Notation, http://www.cl.cam.ac.uk/mgk25/isotime.html
"... Software Cartography: thematic software visualization with consistent layout ‡ ..."
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Software Cartography: thematic software visualization with consistent layout ‡
A Novel Gridbased Visualization Approach for Metabolic Networks with Advanced Focus&Context View
"... Abstract. The universe of biochemical reactions in metabolic pathways can be modeled as a complex network structure augmented with domain specific annotations. Based on the functional properties of the involved reactions, metabolic networks are often clustered into socalled pathways inferred from e ..."
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Abstract. The universe of biochemical reactions in metabolic pathways can be modeled as a complex network structure augmented with domain specific annotations. Based on the functional properties of the involved reactions, metabolic networks are often clustered into socalled pathways inferred from expert knowledge. To support the domain expert in the exploration and analysis process, we follow the wellknown Table Lens metaphor with the possibility to select multiple foci. In this paper, we introduce a novel approach to generate an interactive layout of such a metabolic network taking its hierarchical structure into account and present methods for navigation and exploration that preserve the mental map. The layout places the network nodes on a fixed rectilinear grid and routes the edges orthogonally between the node positions. Our approach supports bundled edge routes heuristically minimizing a given cost function based on the number of bends, the number of edge crossings and the density of edges within a bundle. 1
Coordinate Assignment for Cyclic Level Graphs
"... The Sugiyama framework is the most commonly used concept for visualizing directed graphs. It draws them in a hierarchical way and operates in four phases: cycle removal, leveling, crossing reduction, and coordinate assignment. However, there are situations where cycles must be displayed as such, e. ..."
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Cited by 4 (3 self)
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The Sugiyama framework is the most commonly used concept for visualizing directed graphs. It draws them in a hierarchical way and operates in four phases: cycle removal, leveling, crossing reduction, and coordinate assignment. However, there are situations where cycles must be displayed as such, e. g., distinguished cycles in the biosciences and scheduling processes which repeat in a daily or weekly turn. This excludes the removal of cycles. In their seminal paper Sugiyama et al. introduced recurrent hierarchies as a concept to draw graphs with cycles. However, this concept has not received much attention in the following years. In this paper we supplement our cyclic Sugiyama framework and investigate the coordinate assignment phase. We provide an algorithm which runs in linear time and constructs drawings which have at most two bends per edge and use quadratic area.
Graph drawing techniques for geographic visualization
, 2004
"... Geovisualizers often need to represent data that consists of items related together. Such data sets can be abstracted to a mathematical structure, the graph. A graph contains nodes and edges where the nodes represent the items or concepts of interest, and the edges connect two nodes together accordi ..."
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Cited by 3 (0 self)
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Geovisualizers often need to represent data that consists of items related together. Such data sets can be abstracted to a mathematical structure, the graph. A graph contains nodes and edges where the nodes represent the items or concepts of interest, and the edges connect two nodes together according to some associational scheme. Examples of graph data include: network topologies; maps, where nodes represent
Line crossing minimization on metro maps
, 2007
"... We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V,E), so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying ..."
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Cited by 2 (1 self)
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We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V,E), so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying network, the nodes of G correspond to train stations, an edge connecting two nodes implies that there exists a railway line which connects them, whereas the paths illustrate the lines connecting terminal stations. We call this the metroline crossing minimization problem (MLCM). In contrast to the problem of drawing the underlying graph nicely, MLCM has received fewer attention. It was recently introduced by Benkert et. al in [2]. In this paper, as a first step towards solving MLCM in arbitrary graphs, we study path and tree networks. We examine several variations of the problem for which we develop algorithms for obtaining optimal solutions.
Crossing Minimization in Extended Level Drawings of Graphs
, 2009
"... The most popular method of drawing directed graphs is to place vertices on a set of horizontal or concentric levels, known as level drawings. Level drawings are well studied in Graph Drawing due to their strong application for the visualization of hierarchy in graphs. There are two drawing conventio ..."
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Cited by 2 (2 self)
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The most popular method of drawing directed graphs is to place vertices on a set of horizontal or concentric levels, known as level drawings. Level drawings are well studied in Graph Drawing due to their strong application for the visualization of hierarchy in graphs. There are two drawing conventions: horizontal drawings use a set of parallel lines and radial drawings use a set of concentric circles. In level drawings, edges are only allowed between vertices on different levels. However, many real world graphs exhibit hierarchies with edges between vertices on the same level. In this paper, we initiate the new problem of extended level drawings of graphs, which was addressed as one of the open problems in social network visualization, in particular, displaying centrality values of actors. More specifically, we study minimizing the number of edge crossings in extended level drawings of graphs. The main problem can be formulated as the extended onesided crossing minimization problem between two adjacent levels, as it is folklore with the onesided crossing minimization problem in horizontal drawings. We first show that the extended onesided crossing minimization problem is N Phard for both horizontal and radial drawings, and then present efficient heuristics for minimizing edge crossings in extended level drawings. Our extensive experimental results show that our new methods reduce up to 30 % of edge crossings.
kcolored Pointset Embeddability of Outerplanar Graphs
, 2007
"... This paper addresses the problem of designing drawing algorithms that receive as input a planar graph G, a partitioning of the vertices of G into k different semantic categories V0, · · · , Vk−1, and k disjoint sets S0, · · · , Sk−1 of points in the plane with Vi  = Si  (i ∈ {0, · · · ..."
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This paper addresses the problem of designing drawing algorithms that receive as input a planar graph G, a partitioning of the vertices of G into k different semantic categories V0, · · · , Vk−1, and k disjoint sets S0, · · · , Sk−1 of points in the plane with Vi  = Si  (i ∈ {0, · · · , k − 1}). The desired output is a planar drawing such that the vertices of Vi are mapped onto the points of Si and such that the curve complexity of the edges (i.e. the number of bends along each edge) is kept small. Particular attention is devoted to outerplanar graphs, for which lower and upper bounds on the number of bends in the drawings are established.
Visual Analysis of OnetoMany Matched Graphs
, 2010
"... Motivated by applications of social network analysis and of Web search clustering engines, we describe an algorithm and a system for the display and the visual analysis of two graphs G1 and G2 such that each Gi is defined on a different data set with its own primary relationships and there are secon ..."
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Motivated by applications of social network analysis and of Web search clustering engines, we describe an algorithm and a system for the display and the visual analysis of two graphs G1 and G2 such that each Gi is defined on a different data set with its own primary relationships and there are secondary relationships between the vertices of G1 and those of G2. Our main goal is to compute a drawing of G1 and G2 that makes clearly visible the relations between the two graphs by avoiding their crossings, and that also takes into account some other important aesthetic requirements like number of bends, area, and aspect ratio. Application examples and experiments on the system performances are also presented.