Analysis of a high-dimensional approach to interactive graph drawing

Abstract

Graph drawing is an information visualization technology for illustrating relations between objects. Interactive graph drawing is often important since it is difficult to statically lay out complex graphs. For the interactive drawing of general undirected graphs, we have proposed the high-dimensional approach, which uses static graph layouts in high-dimensional spaces to dynamically find two-dimensional layouts according to user interaction. Although the resulting interactive graph drawing method was found to be fast, other properties of it are not yet clear. In this paper, we analyze the high-dimensional approach to further explore its properties. Specifically, we perform the following two kinds of its analysis: (1) sensitivity analysis for investigating how the high-dimensional approach places graph nodes on the two-dimensional plane; (2) empirical analysis for examining the appropriateness of underlying graph layout methods. The results show that, as an underlying graph layout method, Kruskal and Seery's method based on Torgerson's multidimensional scaling method is more appropriate for the high-dimensional approach than other methods for computing graph layouts in high-dimensional spaces.