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24
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 ..."
Abstract

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.
GEOMI: GEOmetry for Maximum Insight
 In GD05: 13th International Symposium on Graph Drawing
, 2005
"... Abstract. This paper describes the GEOMI system, a visual analysis tool for the visualisation and analysis of large and complex networks. GEOMI provides a collection of network analysis methods, graph layout algorithms and several graph navigation and interaction methods. GEOMI is a new generation ..."
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Cited by 14 (8 self)
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Abstract. This paper describes the GEOMI system, a visual analysis tool for the visualisation and analysis of large and complex networks. GEOMI provides a collection of network analysis methods, graph layout algorithms and several graph navigation and interaction methods. GEOMI is a new generation of visual analysis tools combining graph visualisation techniques with network analysis methods. GEOMI is available from
Multicircular layout of micro/macro graphs
 PROC. 15TH INTL. SYMP. GRAPH DRAWING
, 2007
"... We propose a layout algorithm for micro/macro graphs, i.e. relational structures with two levels of detail. While the microlevel graph is given, the macrolevel graph is induced by a given partition of the microlevel vertices. A typical example is a social network of employees organized into dif ..."
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Cited by 9 (1 self)
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We propose a layout algorithm for micro/macro graphs, i.e. relational structures with two levels of detail. While the microlevel graph is given, the macrolevel graph is induced by a given partition of the microlevel vertices. A typical example is a social network of employees organized into different departments. We do not impose restrictions on the macrolevel layout other than sufficient thickness of edges and vertices, so that the microlevel graph can be placed on top of the macrolevel graph. For the microlevel graph we define a combinatorial multicircular embedding and present corresponding layout algorithms based on edge crossing reduction strategies.
Lombardi Drawings of Graphs
"... We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each ..."
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Cited by 9 (6 self)
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We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs.
Effects of Sociogram Drawing Conventions and Edge Crossings in Social Network Visualization
 Journal of Graph Algorithms and Applications
, 2007
"... This paper describes a withinsubjects experiment. In this experiment, the effects of different spatial layouts on human sociogram perception are examined. We compare the relative effectiveness of five sociogram drawing conventions in communicating underlying network substance, based on user task pe ..."
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Cited by 6 (0 self)
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This paper describes a withinsubjects experiment. In this experiment, the effects of different spatial layouts on human sociogram perception are examined. We compare the relative effectiveness of five sociogram drawing conventions in communicating underlying network substance, based on user task performance and personal preference. We also explore the impact of edge crossings, a widely accepted readability aesthetic. Both objective performance and subjective questionnaire measures are employed in the study. Subjective data are gathered based on the methodology of Purchase et al. [70], while objective data are collected through an online system. We found that 1) both edge crossings and drawing conventions pose significant effects on user preference and task performance of finding groups, but neither has much impact on the perception of actor status. On the other hand, node positioning and angular resolution may be more important in perceiving actor status. In visualizing social networks, it is important to note that the techniques that are highly preferred by users do not necessarily lead to best task performance. 2) subjects have a strong preference of placing nodes on the top or in the center to highlight importance, and clustering nodes in the same group and separating clusters to highlight groups. They have tendency to believe that nodes on the top or in the center are more important, and nodes in close proximity belong to the same group. Some preliminary recommendations for sociogram design and hypotheses about human reading behavior are proposed.
More Flexible Radial Layout
"... We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to concentric circles centered at the origin. Such constraints are typical, e.g., in the layout of social networks, when structural centrality is mapped to geometric centrality or when the primary intenti ..."
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Cited by 5 (3 self)
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We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to concentric circles centered at the origin. Such constraints are typical, e.g., in the layout of social networks, when structural centrality is mapped to geometric centrality or when the primary intention of the layout is the display of the vicinity of a distinguished node. Our approach is based on an extension of stress minimization with a weighting scheme that gradually imposes radial constraints on the intermediate layout during the majorization process, and thus is an attempt to preserve as much information about the graph structure as possible. 1
Global kLevel Crossing Reduction
, 2011
"... Directed graphs are commonly drawn by a four phase framework introduced by Sugiyama et al. in 1981. The vertices are placed on parallel horizontal levels. The edge routing between consecutive levels is computed by solving onesided 2level crossing minimization problems, which are repeated in up and ..."
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Cited by 4 (2 self)
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Directed graphs are commonly drawn by a four phase framework introduced by Sugiyama et al. in 1981. The vertices are placed on parallel horizontal levels. The edge routing between consecutive levels is computed by solving onesided 2level crossing minimization problems, which are repeated in up and down sweeps over all levels. Crossing minimization problems are generally N Phard. We introduce a global crossing reduction, which at any particular time considers all crossings between all levels. Our approach is based on the sifting technique. It yields an improvement of 5 – 10 % in the number of crossings over the levelbylevel onesided 2level crossing reduction heuristics. In addition, it avoids type 2 conflicts which are crossings between edges whose endpoints are dummy vertices. This helps straightening long edges spanning many levels. Finally, the global crossing reduction approach can directly be extended to cyclic, radial, and clustered level graphs achieving similar improvements. The running time is quadratic in the size of the input graph, whereas the common levelbylevel approaches are faster but operate on larger graphs with many dummy vertices for long edges. Submitted:
personal communication
, 2002
"... We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equiangularly spaced around ..."
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Cited by 3 (0 self)
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We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equiangularly spaced around each vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs. Submitted:
A radial adaption of the sugiyama framework for hierarchical graph drawing
, 2006
"... Abstract. In radial drawings of hierarchical graphs the vertices are drawn on concentric circles instead of on horizontal lines as 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 a ..."
Abstract

Cited by 3 (2 self)
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Abstract. In radial drawings of hierarchical graphs the vertices are drawn on concentric circles instead of on horizontal lines as 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 approx. 30% on average. This paper is the last step to complete the framework for drawing hierarchical graphs in a radial fashion. We present three heuristics for crossing reduction in radial level drawings of hierarchical graphs, and also briefly cover extensions of the level assignment step to take advantage of the increasing perimeter of the circles. 1
Grid Sifting: Leveling and Crossing Reduction
, 2011
"... Directed graphs are commonly drawn by the Sugiyama algorithm where first vertices are placed on distinct hierarchical levels and second the vertices on the same level are permuted to reduce the overall number of crossings. Separating these two phases simplifies the algorithms but diminishes the qual ..."
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Cited by 3 (1 self)
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Directed graphs are commonly drawn by the Sugiyama algorithm where first vertices are placed on distinct hierarchical levels and second the vertices on the same level are permuted to reduce the overall number of crossings. Separating these two phases simplifies the algorithms but diminishes the quality of the result. We introduce a combined leveling and crossing reduction algorithm based on sifting, which prioritizes few crossings over few levels. It avoids type 2 conflicts which help to straighten the edges, and has a running time, which is roughly quadratic in the size of the input graph independent of dummy vertices.