G-Space: a linear time graph layout

We describe G-Space (Geodesic Space), a straightforward linear time layout algorithm that draws undirected graphs based purely on their topological features. The algorithm is divided into two phases. The first phase is an embedding of the graph into a 2-D plane using geodesic distances as coordinates. These coordinates are computed with the same process used by HDE (High-Dimensional Embedding) algorithms. In our case we do a Low-Dimensional Embedding (LDE), and directly map the geodesic distances into a two dimensional geometric space. The second phase is the resolution of the many-to-one mappings that frequently occur within the low dimensional embedding. The resulting layout appears to have advantages over existing methods: it can be computed rapidly, and it can be used to answer topological questions quickly and intuitively.