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.

This paper describes the GEOMI system, a visual analysis tool for the visualisation and analysis of large and complex networks. GEOMI

We propose a layout algorithm for micro/macro graphs, i.e. relational structures with two levels of detail. While the micro-level graph is given, the macro-level graph is induced by a given partition of the micro-level vertices. A typical example is a social network of employees organized into different departments. We do not impose restrictions on the macro-level layout other than sufficient thickness of edges and vertices, so that the micro-level graph can be placed on top of the macrolevel graph. For the micro-level graph we define a combinatorial multicircular embedding and present corresponding layout algorithms based on edge crossing reduction strategies.

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.

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:

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

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

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 one-sided 2-level crossing minimization problems, which are repeated in up and down sweeps over all levels. Crossing minimization problems are generally N P-hard. 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 level-by-level one-sided 2-level 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 level-by-level approaches are faster but operate on larger graphs with many dummy vertices for long edges. Submitted:

Abstract. In drawings of hierarchical graphs generated by the conventional Sugiyama framework the vertices are positioned on multiple horizontal level lines. This drawing style which allows edges only between vertices on different levels is well suited for the visualization of a common direction of flow from lower to higher levels in a graph. In this paper we are interested in reordering the vertices on each level line to increase readability of the drawing, i. e., in reducing the number of edge crossings. As novelty, we additionally allow the existence of edges with both end vertices on a common level, which often occur in practice. Experimentally we found out, that we can save about 30 % of the crossings compared to the existing standard heuristic which ignores those edges. 1

This paper describes a user study examining the effects of different spatial layouts on human sociogram perception. The study compares the relative effectiveness of five sociogram drawing conventions in communicating the underlying network substance, based on task performance and user preference. The impact of edge crossings is also explored by using social network specific tasks. Both quantitative and qualitative methods are employed in the study. It was found that 1) both edge crossings and drawing conventions have significant effects on user preference and performance of finding groups, but neither has much impact on the perception of actor importance. On the other hand, node positioning and angular resolution may be more important in perceiving the importance of actors. In visualizing social networks, it is important to note that techniques that are highly preferred by users do not necessarily lead to optimal task performance. 2) the subjects have a strong preference for 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 are also proposed.