Michael Forster

GEOMI: GEOmetry for maximum insight

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 part of a new generation of visual analysis tools combining graph visualisation techniques with network analysis methods. GEOMI is available from http://www.cs.usyd.edu.au/~visual/valacon/geomi/.

Gravisto: graph visualization toolkit

Gravisto, the Graph Visualization Toolkit, is more than a (Java-based) editor for graphs. It includes data structures, graph algorithms, several layout algorithms, and a graph viewer component. As a general toolkit for the visualization and automatic layout of graphs it is extensible with plug-ins and is suited for the integration in other Java-based applications.

Clustered Level Planarity

Planarity is an important concept in graph drawing. It is generally accepted that planar drawings are well understandable. Recently, several variations of planarity have been studied for advanced graph concepts such as k-level graphs [16, 15, 13, 14, 11, 12, 10, 6] and clustered graphs [7, 5]. In k-level graphs, the vertices are partitioned into k levels and the vertices of one level are drawn on a horizontal line. In clustered graphs, there is a recursive clustering of the vertices according to a given nesting relation. In this paper we combine the concepts of level planarity and clustering and introduce clustered k-level graphs. For connected clustered level graphs we show that clustered k-level planarity can be tested in \(\mathcal O(k|v|)\) time.

A fast and simple heuristic for constrained two-level crossing reduction

The one-sided two-level crossing reduction problem is an important problem in hierarchical graph drawing. Because of its NP-hardness there are many heuristics, such as the well-known barycenter and median heuristics. We consider the constrained one-sided two-level crossing reduction problem, where the relative position of certain vertex pairs on the second level is fixed. Based on the barycenter heuristic, we present a new algorithm that runs in quadratic time and generates fewer crossings than existing simple extensions. It is significantly faster than an advanced algorithm by Schreiber [12] and Finnocchi [1,2,6], while it compares well in terms of crossing number. It is also easy to implement.

Radial Level Planarity Testing and Embedding in Linear Time

Every planar graph has a concentric representation based on a breadth first search, see [21]. The vertices are placed on concentric circles and the edges are routed as curves without crossings. Here we take the opposite view. A graph with a given partitioning of its vertices onto k concentric circles is k-radial planar, if the edges can be routed monotonic between the circles without crossings. Radial planarity is a generalisation of level planarity, where the vertices are placed on k horizontal lines. We extend the technique for level planarity testing of [18,17,15,16,12,13] and show that radial planarity is decidable in linear time, and that a radial planar embedding can be computed in linear time.

Crossing minimization in extended level drawings of graphs

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 one-sided crossing minimization problem between two adjacent levels, as it is folklore with the one-sided crossing minimization problem in horizontal drawings. We first show that the extended one-sided crossing minimization problem is NP-hard 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.

BioPath : Exploration and Visualization of Biochemical Pathways

Biochemical reactions in organisms form large and complex networks. Examples are given by the Biochemical Pathways atlas [17] and the well known Boehringer Biochemical Pathways poster [16], see Figure 1. Biochemists are familiar with visual representations of reactions and reaction networks. Automatic visualizations help in understanding the complex relations between the components of the networks and in extracting information from the data. They are very useful for building sophisticated research tools.

Radial coordinate assignment for level graphs

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.