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/.

Combined vs. Separate Views in Matrix-based Graph Analysis and Comparison

“…Given that Erten et al [8] had shown the superiority of a combined node-link view over separate node-link views for multiple graphs, we decided to investigate whether the same held true for the other main visualization method for graphs -the matrix. Thus, our aim was to determine whether a combined matrix would prove superior both in terms of user preference and of performance when compared to juxtaposed matrices.…”

“…Erten et al's [8] work in particular concluded that for collections of small graphs shown as node-link views, a combined view was superior to a juxtaposition of separate graph views for discovering similarities and differences between the set of graphs. Meanwhile, Beck and Diehl's recent work [18] showed the relations within and between multiple revisions of source code, combined into a single matrix view.…”

“…Since adjacency matrices are by definition planar, we examined means of comparing planar views. Erten et al covered three possible ways of laying out small planar graphs [8]; side-by-side, combined into a single planar view, and stacked one upon the other like a deck of cards. The recent IV seminar at Dagstuhl [20] looked at the first two of these options, describing them as juxtaposed and superimposed respectively, and also considered the uses of showing only the differences between data sets, possibly in an abstracted format.…”

A Taxonomy and Survey of Dynamic Graph Visualization

“…Erten et al . [EKLN04], in contrast, allow the same node to have different positions on the layers; to preserve the mental map, they use an adapted force‐directed layout algorithm that moves the same nodes to at least similar positions across layers (Figure , relaxed positions). Groh et al .…”

“…Similarly, Brandes and Corman [BC03] depict nodes as cylinders, but also add transparent planes that help discern the stacked layers (Figure 8, fixed positions). Erten et al [EKLN04], in contrast, allow the same node to have different positions on the layers; to preserve the mental map, they use an adapted force-directed layout algorithm that moves the same nodes to at least similar positions across layers (Figure 8, relaxed positions). Groh et al [GHW09] extend this approach by abstracting from nodes and links: they just use the connections between the same nodes of different layers (i.e.…”