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 vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs.Comment: Expanded version of paper appearing in the 18th International Symposium on Graph Drawing (GD 2010). 13 pages, 7 figure

Drawing Trees with Perfect Angular Resolution and Polynomial Area

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.Comment: 30 pages, 17 figure

Planar and Poly-Arc Lombardi Drawings

In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs, noting that every graph has a smooth 2-Lombardi drawing. We show that every planar graph has a smooth planar 3-Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings.Comment: Expanded version of paper appearing in the 19th International Symposium on Graph Drawing (GD 2011). 16 pages, 8 figure

Affective graphs: the visual appeal of linked data

The essence and value of Linked Data lies in the ability of humans and machines to query, access and reason upon highly structured and formalised data. Ontology structures provide an unambiguous description of the structure and content of data. While a multitude of software applications and visualization systems have been developed over the past years for Linked Data, there is still a significant gap that exists between applications that consume Linked Data and interfaces that have been designed with significant focus on aesthetics. Though the importance of aesthetics in affecting the usability, effectiveness and acceptability of user interfaces have long been recognised, little or no explicit attention has been paid to the aesthetics of Linked Data applications. In this paper, we introduce a formalised approach to developing aesthetically pleasing semantic web interfaces by following aesthetic principles and guidelines identified from literature. We apply such principles to design and develop a generic approach of using visualizations to support exploration of Linked Data, in an interface that is pleasing to users. This provides users with means to browse ontology structures, enriched with statistics of the underlying data, facilitating exploratory activities and enabling visual query for highly precise information needs. We evaluated our approach in three ways: an initial objective evaluation comparing our approach with other well-known interfaces for the semantic web and two user evaluations with semantic web researchers

Using Graph Layout to Visualize Train Interconnection Data

We are concerned with the problem of visualizing interconnections in railroad systems. The real-world systems we have to deal with contain connections of thousands of trains. To visualize such a system from a given set of time tables a so-called train graph is used. It contains a vertex for each station met by any train, and one edge between every pair of vertices connected by some train running from one station to the other without halting in between

Visualisierung biochemischer Reaktionsnetze

In dieser Arbeit werden Anforderungen an die Darstellung biochemischer Reaktionsnetze untersucht und die Netze unter dem Gesichtspunkt der Visualisierung modelliert. Anschliessend wird ein Algorithmus zum Zeichnen biochemischer Reaktionsnetze entwickelt und analysiert.In this dissertation we investigate the requirements for the visualisation of biochemical reaction networks. We compose a model for these networks that lends itself to visualisation and develop and analyse an algorithm to create drawings of the networks