Stub Bundling and Confluent Spirals for Geographic Networks

Edge bundling is a technique to reduce clutter by routing parts of several edges along a shared path. In particular, it is used for visualization of geographic networks where vertices have fixed coordinates. Two main drawbacks of the common approach of bundling the interior of edges are that (i) tangents at endpoints deviate from the line connecting the two endpoints in an uncontrolled way and (ii) there is ambiguity as to which pairs of vertices are actually connected. Both severely reduce the interpretability of geographic network visualizations. We therefore propose methods that bundle edges at their ends rather than their interior. This way, tangents at vertices point in the general direction of all neighbors of edges in the bundle, and ambiguity is avoided altogether. For undirected graphs our approach yields curves with no more than one turning point. For directed graphs we introduce a new drawing style, confluent spiral drawings, in which the direction of edges can be inferred from monotonically increasing curvature along each spiral segment.