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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.
Completely connected clustered graphs
 IN PROC. 29TH INTL. WORKSHOP ON GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE (WG 2003), VOLUME 2880 OF LNCS
, 2003
"... Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove ..."
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Cited by 14 (1 self)
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Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove that a completely connected clustered graph is cplanar if and only if the underlying graph is planar. Further, we investigate the influence of the root of the inclusion tree to the choice of the outer face of the underlying graph and vice versa.
Characterization of unlabeled level planar trees
 14TH SYMPOSIUM ON GRAPH DRAWING (GD), VOLUME 4372 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓj = {(x, j)  x ∈ R}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓj forms a labeling of the vertices. Such a graph G with the labeling φ is called an nlevel gr ..."
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Cited by 13 (7 self)
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Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓj = {(x, j)  x ∈ R}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓj forms a labeling of the vertices. Such a graph G with the labeling φ is called an nlevel graph and is said to be nlevel planar if it can be drawn with straightline edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are nlevel planar regardless of their labeling. We call such trees unlabeled level planar (ULP). Our contributions are threefold. First, we provide a complete characterization of ULP trees in terms of a pair of forbidden subtrees. Second, we show how to draw ULP trees in linear time. Third, we provide a linear time recognition algorithm for ULP trees.
Visualizing large graphs with compoundfisheye views and treemaps
 In 12th Symposium on Graph Drawing (GD
, 2004
"... Abstract. Compoundfisheye views are introduced as a method for the display and interaction with large graphs. The method relies on a hierarchical clustering of the graph, and a generalization of the traditional fisheye view, together with a treemap representation of the cluster tree. 1 ..."
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Cited by 10 (1 self)
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Abstract. Compoundfisheye views are introduced as a method for the display and interaction with large graphs. The method relies on a hierarchical clustering of the graph, and a generalization of the traditional fisheye view, together with a treemap representation of the cluster tree. 1
Planaritypreserving clustering and embedding for large planar graphs
 In Graph Drawing (GD'99
, 1999
"... Abstract. In this paper we present a novel approach for clusterbased drawing of large planar graphs that maintains planarity. Our technique works for arbitrary planar graphs and produces a clustering which satisfies the conditions for compoundplanarity (cplanarity). Using the clustering, we obtai ..."
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Cited by 10 (3 self)
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Abstract. In this paper we present a novel approach for clusterbased drawing of large planar graphs that maintains planarity. Our technique works for arbitrary planar graphs and produces a clustering which satisfies the conditions for compoundplanarity (cplanarity). Using the clustering, we obtain a representation of the graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. At the same time, the difference between two graphs on neighboring layers of the hierarchy is small, thus preserving the viewer's mental map. The overall running time of the algorithm is O(n log n), where n is the number of vertices of graph G.
Symmetric Drawings of Triconnected Planar Graphs
 Proc. of SODA 2002
, 2002
"... Abstract: This paper proves that every internally triconnected hierarchical plane graph with the outer facial cycle drawn as a convex polygon admits a convex drawing. We present an algorithm which constructs such a drawing. This extends the previous known result that every hierarchical plane graph a ..."
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Cited by 9 (7 self)
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Abstract: This paper proves that every internally triconnected hierarchical plane graph with the outer facial cycle drawn as a convex polygon admits a convex drawing. We present an algorithm which constructs such a drawing. This extends the previous known result that every hierarchical plane graph admits a straightline drawing.
Improving the readability of clustered social networks using node duplication
 IEEE Transactions on Visualization and Computer Graphics
, 2008
"... Abstract—Exploring communities is an important task in social network analysis. Such communities are currently identified using clustering methods to group actors. This approach often leads to actors belonging to one and only one cluster, whereas in real life a person can belong to several communiti ..."
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Cited by 8 (1 self)
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Abstract—Exploring communities is an important task in social network analysis. Such communities are currently identified using clustering methods to group actors. This approach often leads to actors belonging to one and only one cluster, whereas in real life a person can belong to several communities. As a solution we propose duplicating actors in social networks and discuss potential impact of such a move. Several visual duplication designs are discussed and a controlled experiment comparing network visualization with and without duplication is performed, using 6 tasks that are important for graph readability and visual interpretation of social networks. We show that in our experiment, duplications significantly improve communityrelated tasks but sometimes interfere with other graph readability tasks. Finally, we propose a set of guidelines for deciding when to duplicate actors and choosing candidates for duplication, and alternative ways to render them in social network representations. Index Terms—Clustering, Graph Visualization, Node Duplications, Social Networks. 1
Radial coordinate assignment for level graphs
 Proc. Computing and Combinatorics, COCOON 2005, volume 3595 of LNCS
, 2005
"... Abstract. We present a simple linear time algorithm for drawing level graphs with a given ordering of the vertices within each level. The algorithm draws in a radial fashion without changing the vertex ordering, and therefore without introducing new edge crossings. Edges are drawn as sequences of sp ..."
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Cited by 6 (3 self)
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Abstract. We present a simple linear time algorithm for drawing level graphs with a given ordering of the vertices within each level. The algorithm draws in a radial fashion without changing the vertex ordering, and therefore without introducing new edge crossings. Edges are drawn as sequences of spiral segments with at most two bends. 1
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.
Monotone drawings of planar graphs
"... Let G be a graph drawn in the plane so that its edges are represented by xmonotone curves, any pair of which cross an even number of times. We show that G can be redrawn in such a way that the xcoordinates of the vertices remain unchanged and the edges become noncrossing straightline segments. ..."
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Cited by 6 (1 self)
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Let G be a graph drawn in the plane so that its edges are represented by xmonotone curves, any pair of which cross an even number of times. We show that G can be redrawn in such a way that the xcoordinates of the vertices remain unchanged and the edges become noncrossing straightline segments.