We present a novel approach to the aesthetic drawing of undirected graphs. The method has two phases: first embed the graph in a very high dimension and then project it into the 2-D plane using PCA. Experiments we have carried out show the ability of the method to draw graphs of 10 nodes in few seconds. The new method appears to have several advantages over classical methods, including a significantly better running time, a useful inherent capability to exhibit the graph in various dimensions, and an effective means for interactive exploration of large graphs.

In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A k-stack (resp...

We describe a method for the visualization of information units on spherical domains which is employed in the banking industry for risk analysis, stock prediction and other tasks. The system is based on a quantification of the similarity of related objects that governs the parameters of a mass-spring system. Unlike existing approaches we initialize all information units onto the inner surface of two concentric spheres and attach them with springs to the outer sphere. Since the spring stiffnesses correspond to the computed similarity measures, the system converges into an energy minimum which reveals multidimensional relations and adjacencies in terms of spatial neighborhoods. Depending on the application scenario our approach supports different topological arrangements of related objects. In order to cope with large data sets we propose a blobby clustering mechanism that enables encapsulation of similar objects by implicit shapes. In addition, we implemented various interaction techniques allowing semantic analysis of the underlying data sets. Our prototype system IVORY is written in JAVA, and its versatility is illustrated by an example from financial service providers.

A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queue-number. A three-dimensional (straight- line grid) drawing of a graph represents the vertices by points in Z and the edges by non-crossing line-segments. This paper contributes three main results: (1) It is proved that the minimum volume of a certain type of three-dimensional drawing of a graph G is closely related to the queue-number of G. In particular, if G is an n-vertex member of a proper minor-closed family of graphs (such as a planar graph), then G has a O(1) O(1) O(n) drawing if and only if G has O(1) queue-number.

We present a novel hierarchical force-directed method for drawing large graphs. The algorithm produces a graph embedding in an Euclidean space E of any dimension. A two or three dimensional drawing of the graph is then obtained by projecting a higher-dimensional embedding into a two or three dimensional subspace of E. Projecting high-dimensional drawings onto two or three dimensions often results in drawings that are "smoother" and more symmetric. Among the other notable features of our approach are the utilization of a maximal independent set filtration of the set of vertices of a graph, a fast energy function minimization strategy, e#cient memory management, and an intelligent initial placement of vertices. Our implementation of the algorithm can draw graphs with tens of thousands of vertices using a negligible amount of memory in less than one minute on a mid-range PC. 1 Introduction Graphs are common in many applications, from data structures to networks, from software engineering...

We present a preprocessor for the spring embedder graph drawing method and show its use in speeding up the automatic layout of three-dimensional visualizations of WWW sites. Spring embedding is a widely used method for visualizing the connections in WWW maps, as it can typically produce a reasonable layout for most general graphs. However, the technique does not scale well and to improve the performance when dealing with large graphs various optimisations have been developed. Our preprocessor is a new optimization method that attempts to obtain a reasonably good initial drawing to be then used by the spring embedder. This initial drawing has edge lengths that are approximately equal along with a minimum node separation. This produces a layout that is closer to the final drawing than a random scattering of nodes and so allows fewer invocations of the spring embedder to produce an equally stable drawing.

The following paper describes a framework for the visualization and analysis of economic data. It can be employed in the context of risk analysis, stock prediction and other tasks being important in the context of banking. The system bases on a quantification of the similarity of related objects, which governs the parameters of a mass-spring system, organized as two concentric spheres. More specifically, we initialize all information units onto the surface of the inner sphere and attach them with springs to the outer sphere. Since the spring stiffnesses correspond to the computed similarity measures, the system converges into an energy minimum, which reveals multidimensional relations and adjacencies in terms of spatial neighborhoods. In order to simplify complex setups we propose an additional clustering algorithm for postprocessing. Furthermore, depending on the application scenario we support different topologic arrangements of related objects. In addition, we implemented various interaction techniques allowing semantic analysis of the underlying data sets. The versatility of our approach is illustrated by two examples, namely a comparison of agricultural productivity and an analysis of the relation between interest rates and other economic data.

The topic of skeletal animation and its associated techniques have previously been applied in the area of animating computer-generated characters for motion pictures and computer games. This thesis investigates the use of similar techniques in the scope of exploring three-dimensional visualisations of relational networks (graphs). A system

In this paper we present a method to extract qualitative information from any classification model that uses decision regions to generalize (e.g., feedforward neural nets, SVMs, etc). The method's complexity is independent of the dimensionality of the input data or model, making it computationally feasible for the analysis of even very high-dimensional models. The qualitative information extracted by the method can be directly used to analyze the classification strategies employed by a model, and also to compare strategies across diferent model types.

Abstract. In this paper we discuss a useful family of graph drawing algorithms, characterized by their ability to draw graphs in one dimension. We define the spe-cial requirements from such algorithms and show how several graph drawing tech-niques can be extended to handle this task. In particular, we suggest a novel op-timization algorithm that facilitates using the Kamada and Kawai model [17] for producing one-dimensional layouts. The most important application of the algo-rithms seems to be in achieving graph drawing by axis separation, where each axis of the drawing addresses different aspects of aesthetics.