Effects of Curved Lines on Force-Directed Graphs.

The most common methods for simplifying force-directed graphs are edge-bundling and edge routing. Both of these methods can be done with curved, rather than straight, lines which some researchers have argued. Curved lines have been offered as a solution for clarifying edge resolution. Curved lines were originally thought to be more aesthetically pleasing. 32 computer science students were surveyed and asked questions about straight and curved line graphs. Research conducted by Xu et al. and this study suggests that curved lines make a graph more difficult to understand and slower to read. Research also suggests that curved lines are no more aesthetically pleasing than straight lines. Situations may exist where curved lines are beneficial to a graph’s readability, but it is unclear due to uncontrolled variables in this study. Further study could reveal circumstances when curved lines would be beneficial

Lombardi Drawings of Graphs

We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs.Comment: Expanded version of paper appearing in the 18th International Symposium on Graph Drawing (GD 2010). 13 pages, 7 figure

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

Drawing Trees with Perfect Angular Resolution and Polynomial Area

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.Comment: 30 pages, 17 figure

Performance comparisons between force-directed algorithms on structured data analysis

© 2017 IEEE. Evaluation on the performance of relevant force-directed algorithms is still a challenge, since layout quality is largely relying on personal judgement and/or methods' input parameters, and most aesthetics criteria conflict with each other. This study conducts the performance measurements of four algorithms in terms of seven commonly applied aesthetic criteria and demonstrates the experimental framework

Improving Automated Layout Techniques for the Production of Schematic Diagrams

This thesis explores techniques for the automated production of schematic diagrams, in particular those in the style of metro maps. Metro map style schematics are used across the world, typically to depict public transport networks, and therefore benefit from an innate level of user familiarity not found with most other data visualisation styles. Currently, this style of schematic is used infrequently due to the difficulties involved with creating an effective layout – there are no software tools to aid with the positioning of nodes and other features, resulting in schematics being produced by hand at great expense of time and effort. Automated schematic layout has been an active area of research for the past decade, and part of our work extends upon an effective current technique – multi-criteria hill climbing. We have implemented additional layout criteria and clustering techniques, as well as performance optimisations to improve the final results. Additionally, we ran a series of layouts whilst varying algorithm parameters in an attempt to identify patterns specific to map characteristics. This layout algorithm has been implemented into a custom-written piece of software running on the Android operating system. The software is targeted at tablet devices, using their touch-sensitive screens with a gesture recognition system to allow users to construct complex schematics using sequences of simple gestures. Following on from this, we present our work on a modified force-directed layout method capable of producing fast, high-quality, angular schematic layouts. Our method produces superior results to the previous octilinear force-directed layout method, and is capable of producing results comparable to many of the much slower current approaches. Using our force-directed layout method we then implemented a novel mental map preservation technique which aims to preserve node proximity relations during optimisation; we believe this approach provides a number of benefits over the the more common method of preserving absolute node positions. Finally, we performed a user study on our method to test the effect of varying levels of mental map preservation on diagram comprehension

Graph Layout Performance Comparisons of Force-Directed Algorithms

© 2018 Totem Publisher, Inc. All rights reserved. Due to force-directed algorithms’ capabilities of producing aesthetically pleasing graph layouts, which follow metrics for graph drawing aesthetics, these layouts have become the most common methods in the practical data visualization area. However, evaluating the performance of relevant algorithms remains a challenge, since graph layout quality is largely relying on aspects such as human intuition, personal judgment and methods’ pre-setting parameters. In addition, most aesthetics criteria of graph drawing conflict with each other. This study evaluated the performance measurements of four force-directed algorithms in terms of seven commonly applied aesthetic criteria based on practical raw data collected, and demonstrated the experimental framework. The early outcomes compared twenty final graph layouts and gave empirical evidences; the study may assist with future detailed force-directed algorithms selection based on users’ specific requirements