Cologne Excellence Cluster on Cellular Stress Responses in Aging Associated Diseases
Graph Drawing E-print ArchiveNot a member yet
1225 research outputs found
Sort by
Visualizing Large Hierarchically Clustered Graphs with a Landscape Metaphor
No full textIndroduction.
Large graphs appear in many application domains. Their analysis can be done automatically by machines, for which the graph size is less of a problem, or, especially for exploration tasks, visually by humans. The graph drawing literature contains many efficient methods for visualizing large graphs, see e.g. [4, Chapter 12], but for large graphs it is often useful to first compute a sequence of coarser and more abstract representations by grouping vertices recursively using a hierarchical clustering algorithm. Then the task is to compute an overview picture of the graph based on a given cluster hierarchy, such that details of the graph, e.g., within clusters, remain visible on demand
Drawing Cubic Graphs with the Four Basic Slopes
No full textWe show that every cubic graph can be drawn in the plane with straight-line edges using only the four basic slopes, {0, π/4, π/2, 3π/4}. We also prove that four slopes have this property if and only if we can draw K4 with them
Monotone Crossing Number
No full textThe monotone crossing number of G is defined as the smallest number of crossing points in a drawing of G in the plane, where every edge is represented by an x-monotone curve, that is, by a connected continuous arc with the property that every vertical line intersects it in at most one point. It is shown that this parameter can be strictly larger than the classical crossing number cr(G), but it is bounded from above by 2cr2 (G). This is in sharp contrast with the behavior of the rectilinear crossing number, which cannot be bounded from above by any function of cr(G)
Planar and Poly-arc Lombardi Drawings
No full textIn 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
Monotone Drawings of Graphs with Fixed Embedding
No full textA drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most 4n − 10 bends in total; such a drawing can be computed in linear time and requires polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges, and we show that biconnected embedded planar graphs and outerplane graphs always admit such drawings, which can be computed in linear time
The Open Graph Archive: A Community-Driven Effort
No full textA graphbase, a term coined by Knuth [7], is a database of graphs and computer programs that generate, analyze, manipulate, and visualize graphs. The terms graph library and graph archive are often used as synonyms for this term. Our vision is to provide an infrastructure and quality standards for a public graphbase, named the Open Graph Archive, that is accessible to researchers and other interested parties around the world via the worldwide web. This paper describes the current work undertaken towards this goal; the paper is also intended to be a call for participation since this will be a community-driven effort where most of the content will be provided by users of the system
Viewport for Component Diagrams
No full textThis paper describes a viewport technique for use in the visualization of large graphs, e.g. UML component diagrams. This technique should help to work with complex diagrams (hundreds or thousands of components) by highlighting details of the important parts of the diagram and their related surroundings without losing the global perspective. To avoid visual clutter it uses clusters of interfaces and components
Planar Open Rectangle-of-Influence Drawings with Non-aligned Frames
No full textA straight-line drawing of a graph is an open weak rectangle-of-influence (RI) drawing, if there is no vertex in the relative interior of the axis-parallel rectangle induced by the end points of each edge. No algorithm is known to test whether a graph has a planar open weak RI-drawing, not even for inner triangulated graphs. In this paper, we study RI-drawings that must have a non-aligned frame, i.e., the graph obtained from removing the interior of every filled triangle is drawn such that no two vertices have the same coordinate. We give a polynomial algorithm to test whether an inner triangulated graph has a planar open weak RI-drawing with non-aligned frame
Graph Visualization
No full textBlack and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations. A variety of ingredients, including color, shape, 3D, shading, and interaction can be used to this end. In this invited talk an overview is given of work on graph visualization of the visualization group of Eindhoven University of Technology, The Netherlands. A wide variety of examples is shown and discussed using demos and animations
TGI-EB: A New Framework for Edge Bundling Integrating Topology, Geometry and Importance
No full textEdge bundling methods became popular for visualising large dense networks; however, most of previous work mainly relies on geometry to define compatibility between the edges. In this paper, we present a new framework for edge bundling, which tightly integrates topology, geometry and importance. In particular, we introduce new edge compatibility measures, namely importance compatibility and topology compatibility. More specifically, we present four variations of force directed edge bundling method based on the framework: Centrality-based bundling, Radial bundling, Topology-based bundling, and Orthogonal bundling. Our experimental results with social networks, biological networks, geographic networks and clustered graphs indicate that our new framework can be very useful to highlight the most important topological skeletal structures of the input networks