Simultaneous Graph Drawing: Layout Algorithms and Visualization Schemes

Abstract

Abstract. In this paper we consider the problem of drawing and displaying a series of related graphs, i.e., graphs that share all, or parts of the same vertex set. We designed and implemented three different algorithms for simultaneous graph drawing and three different visualization schemes. The algorithms are based on a modification of the force-directed algorithm that allows us to take into account vertex weights and edge weights in order to achieve mental map preservation while obtaining individually readable drawings. The implementation is in Java and the system can be downloaded at http://simg.cs.arizona.edu/.

Temporal Multivariate Networks

“…By changing the weights of these inter-timestep edges one can emphasize stability (make inter-timestep edges very strong) or readability (make inter-timestep edges very weak). Such approaches [35,36,32,39] generally use modified versions of traditional static layout algorithms directly, but often induce high memory usage and complexity because all timesteps are loaded at once. They are also only applicable to offline graph drawing, as the entire data range is needed at the beginning.…”

Simultaneous Embedding of Planar Graphs with Few Bends

“…Counter-examples for pairs of general planar graphs, pairs of outer-planar graphs, and triples of paths are also presented there. Modified force-directed algorithms are used in [1,8] to simultaneously visualize general graphs, while attempting to preserve the user's mental map and obtaining readable individual drawings.…”

An Interactive Multi-user System for Simultaneous Graph Drawing

“…Modified force-directed methods are used to visualize general graphs simultaneously such that the mental map is preserved up in [7]. Conceptually, the problem of simultaneously embedding graphs is the reverse of the geometric thickness problem [5].…”