8 research outputs found
A Coloring Algorithm for Disambiguating Graph and Map Drawings
Drawings of non-planar graphs always result in edge crossings. When there are
many edges crossing at small angles, it is often difficult to follow these
edges, because of the multiple visual paths resulted from the crossings that
slow down eye movements. In this paper we propose an algorithm that
disambiguates the edges with automatic selection of distinctive colors. Our
proposed algorithm computes a near optimal color assignment of a dual collision
graph, using a novel branch-and-bound procedure applied to a space
decomposition of the color gamut. We give examples demonstrating the
effectiveness of this approach in clarifying drawings of real world graphs and
maps
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
Scalability considerations for multivariate graph visualization
Real-world, multivariate datasets are frequently too large to show in their entirety on a visual display. Still, there are many techniques we can employ to show useful partial views-sufficient to support incremental exploration of large graph datasets. In this chapter, we first explore the cognitive and architectural limitations which restrict the amount of visual bandwidth available to multivariate graph visualization approaches. These limitations afford several design approaches, which we systematically explore. Finally, we survey systems and studies that exhibit these design strategies to mitigate these perceptual and architectural limitations
Circle-Representations of Simple 4-Regular Planar Graphs
Lovász conjectured that every connected 4-regular planar graph G admits a realization as a system of circles, i.e., it can be drawn on the plane utilizing a set of circles, such that the vertices of G correspond to the intersection and touching points of the circles and the edges of G are the arc segments among pairs of intersection and touching points of the circles. In this paper, (a) we affirmatively answer Lovász's conjecture, if G is 3-connected, and, (b) we demonstrate an infinite class of connected 4-regular planar graphs which are not 3-connected and do not admit a realization as a system of circles
On the usability of Lombardi graph drawings
A recent line of work in graph drawing studies Lombardi drawings, i.e., drawings with circular-arc edges and perfect angular resolution at vertices. Little is known about the effects of curved edges versus straight edges in typical graph reading tasks. In this paper we present the first user evaluation that empirically measures the readability of three different layout algorithms (traditional spring embedder and two recent near-Lombardi force-based algorithms) for three different tasks (shortest path, common neighbor, vertex degree). The results indicate that, while users prefer the Lombardi drawings, the performance data do not present such a positive picture
Planar Lombardi Drawings for Subcubic Graphs
We prove that every planar graph with maximum degree three has a planar
drawing in which the edges are drawn as circular arcs that meet at equal angles
around every vertex. Our construction is based on the Koebe-Thurston-Andreev
circle packing theorem, and uses a novel type of Voronoi diagram for circle
packings that is invariant under Moebius transformations, defined using
three-dimensional hyperbolic geometry. We also use circle packing to construct
planar Lombardi drawings of a special class of 4-regular planar graphs, the
medial graphs of polyhedral graphs, and we show that not every 4-regular planar
graph has a Lombardi drawing. We have implemented our algorithm for 3-connected
planar cubic graphs.Comment: 15 pages, 9 figure
LAY summaries for Cortex articles
Force-directed layout algorithms produce graph drawings by resolving a system
of emulated physical forces. We present techniques for using social gravity as
an additional force in force-directed layouts, together with a scaling
technique, to produce drawings of trees and forests, as well as more complex
social networks. Social gravity assigns mass to vertices in proportion to their
network centrality, which allows vertices that are more graph-theoretically
central to be visualized in physically central locations. Scaling varies the
gravitational force throughout the simulation, and reduces crossings relative
to unscaled gravity. In addition to providing this algorithmic framework, we
apply our algorithms to social networks produced by Mark Lombardi, and we show
how social gravity can be incorporated into force-directed Lombardi-style
drawings.Comment: GD201