Christian Pich

CENTRALITY ESTIMATION IN LARGE NETWORKS

Centrality indices are an essential concept in network analysis. For those based on shortest-path distances the computation is at least quadratic in the number of nodes, since it usually involves solving the single-source shortest-paths (SSSP) problem from every node. Therefore, exact computation is infeasible for many large networks of interest today. Centrality scores can be estimated, however, from a limited number of SSSP computations. We present results from an experimental study of the quality of such estimates under various selection strategies for the source vertices.

Eigensolver methods for progressive multidimensional scaling of large data

We present a novel sampling-based approximation technique for classical multidimensional scaling that yields an extremely fast layout algorithm suitable even for very large graphs. It produces layouts that compare favorably with other methods for drawing large graphs, and it is among the fastest methods available. In addition, our approach allows for progressive computation, i.e. a rough approximation of the layout can be produced even faster, and then be refined until satisfaction.

An Experimental Study on Distance-Based Graph Drawing

In numerous application areas, general undirected graphs need to be drawn, and force-directed layout appears to be the most frequent choice. We present an extensive experimental study showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms based on variants of multidimensional scaling is to be preferred because of their efficiency, reliability, and even simplicity. We also hope that details in the design of our study help advance experimental methodology in algorithm engineering and graph drawing, independent of the case at hand.

Visualizing internet evolution on the autonomous systems level

We propose a visualization approach for large dynamic graph structures with high degree variation and low diameter. In particular, we reduce visual complexity by multiple modes of representation in a single-level visualization rather than abstractions of lower levels of detail. This is useful for non-interactive display and eases dynamic layout, which we address in the online scenario. Our approach is illustrated on a family of large networks featuring all of the above structural characteristics, the physical Internet on the autonomous systems level over time.

GraphML transformation

The efforts put into XML-related technologies have exciting consequences for XML-based graph data formats such as GraphML. We here give a systematic overview of the possibilities offered by XSLT style sheets for processing graph data, and illustrate that many basic tasks required for tools used in graph drawing can be implemented by means of style sheets, which are convenient to use, portable, and easy to customize.

GXL to GraphML and Vice Versa with XSLT

We explore the issues involved in converting graph data stored in GXL or GraphML into each other. It turns out that XSLT provides a simple, portable, and effective mechanism for format conversion in either direction. As a by-product, some subtle differences between the formats become apparent.

Affiliation dynamics with an application to movie-actor biographies

We propose a visualization approach for dynamic affiliation networks in which events are characterized by a set of descriptors. It uses a radial ripple metaphor to display the passing of time and conveys relations among the different constituents through appropriate layout. Our method is particularly suitable when assuming an egocentric perspective, and we illustrate it on movie-actor biographies.

More flexible radial layout

We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to the circumferences of a set of concentric circles around the origin. Such constraints frequently occur in the layout of social or policy 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. We extend stress majorization by a weighting scheme which imposes radial constraints on the layout but also tries to preserve as much information about the graph structure as possible.

Visual analysis of importance and grouping in software dependency graphs

Understanding dependencies between components is a key task in software engineering. We present a method for the display and visual analysis of dependency graphs occurring in large software systems. Our layout approach takes into account similarity and importance of the system components and additional grouping information; using efficient algorithms based on linear algebra, it scales to very large dependency graphs. We apply our method to two real-world software systems and present the results.

Drawing directed graphs clockwise

We present a method for clockwise drawings of directed cyclic graphs. It is based on the eigenvalue decomposition of a skew-symmetric matrix associated with the graph and draws edges clockwise around the center instead of downwards, as in the traditional hierarchical drawing style. The method does not require preprocessing for cycle removal or layering, which often involves computationally hard problems. We describe an efficient algorithm which produces optimal solutions, and we present some application examples.