Journal of Graph Algorithms and Applications http://jgaa.info/ vol. 8, no. 2, pp. 195–214 (2004) Graph Drawing by High-Dimensional Embedding David Harel Dept. of Computer Science and Applied Mathematics The Weizmann Institute of Science, Rehovot, Israel http://www.wisdom.weizmann.ac.il/˜dharel/ dharel@wisdom.weizmann.ac.il Yehuda Koren AT&T Labs – Research Florham Park, NJ 07932 http://www.research.att.com/˜yehuda/ yehuda@research.att.com Abstract We present a novel approach to the aesthetic drawing of undirected graphs. The method has two phases: first embed the graph in a very high dimension and then project it into the 2-D plane using principal compo- nents analysis. Running time is linear in the graph size, and experiments we have carried out show the ability of the method to draw graphs of 10 5 nodes in few seconds. The new method appears to have several advan- tages over classical methods, including a significantly better running time, a useful inherent capability to exhibit the graph in various dimensions, and an effective means for interactive exploration of large graphs. Article Type Communicated by Submitted Revised Regular Paper Xin He March 2003 November 2003 An earlier version of this work appeared in: Proc. 10th Graph Drawing (GD’02), LNCS 2528, pp. 207–219, Springer-Verlag, 2002.