A graph processing module is described for producing a visualization of a layered graph. The graph processing module operates by: bundling edges in the layered graph to produce respective edge bundles; ordering the edges associated with the edge bundles to reduce edge crossings; straightening the edges; and separating the edges in the edges bundles with respect to each other. The graph processing module can operate on a layered graph produced by the Sugiyama algorithm or some other technique, reducing clutter in the layered graph and thus improving a user's understanding of the layered graph.