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Current graph drawing algorithms enable the creation of two dimensional node-link diagrams of huge graphs. However, for graphs with low diameter (of which "small world" graphs are a subset) these techniques begin to break down visually even when the graph has only a few hundred nodes. Typical algorithms produce images where nodes clump together in the center of the screen, making it hard to discern structure and follow paths. This paper describes a solution to this problem, which uses a global edge metric to determine a subset of edges that capture the graph's intrinsic clustering structure. This structure is then used to create an embedding of the graph, after which the remaining edges are added back in. We demonstrate applications of this technique to a number of real world examples.

This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry and computer graphics closer together.