Graph Drawing by High-Dimensional Embedding

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 components 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 advantages 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.

Information Visualization for Tourist and Travelling in Indonesia

“…To create a good graph for this tourist application, a method of drawing graphs that can accelerate the search for the shortest route is required. A high-dimensional embedding method to describe the graph and using a goal-directed search to accelerate the computation of the Dijkstra's algorithm is used [8]. Edge is a path in the graph representation.…”

Large Quasi-Tree Drawing: A Neighborhood Based Approach

“…Among them, the most famous is based on improvements of force directed methods ( [15,16,2]). Another approach consists in representing the graph as a matrix and using linear algebra techniques ( [18,27]). Finally, a recent technique is based on topologies detection and the use of an appropriate algorithm for each topology ( [1,4,3]).…”

“…Harel and Koren give in [18] an algorithm consisting in computing an m-dimensional embedding of the graph (typically m is set to 50) and then to project this embedding into 2 or 3 dimensions. To define these m axis, the authors compute a set {p 1 , p 2 , ..., p m } of m pivots (one for each dimension) such that the distance between all p i is maximized.…”

“…They look for proper subgraphs that are trees, biconnected components, HDE [18] suitable graphs (for more details see [4]), complete graphs and finally use strength [6]. Archambault et al adapted this pipeline to the special properties of quasi-tree graphs in [3].…”

Generalizing Geometric Graphs

“…Visualization of these networks is a key to assessing the inherent graph-based information. There are several methods for computing layouts of huge graphs with millions of vertices within a few minutes [21,23,19].…”