Stub Bundling and Confluent Spirals for Geographic Networks

Abstract

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. Research supported in part by DFG under grant GRK 1024. We are grateful to Sabine Cornelsen for valuable comments and suggestions on earlier drafts of this paper.

An Evolutionary Algorithm for an Optimization Model of Edge Bundling

“…It is hard to establish which nodes are connected to each other in those layouts. Some exceptions are the stub bundling [9] and the sideknot [2] approaches (Figure 17b,c), which are more similar to EEB. They join only adjacent edges with the aim of indicating directions at the endpoints of the edges, highlighting node-level connections and tracing individual edges.…”

“…Nocaj and Brandes [9] refined the technique of [2] and proposed a method called stub bundling that joins only edges that share the same endpoint. The method has the aim of visualizing unambiguous graphs and retrieving the exact source and target of each edge.…”

“…Even though the methods in [2,9] efficiently produce bundles with only adjacent edges, neither of them has the aim of explicitly minimizing the number of bundles. In order to achieve this goal, it may be needful to formulate an optimization problem having decision variables, constraints and objectives.…”

“…Bundles can be separated into two types, those composed of (i) only edges sharing a common end node (bundling of only adjacent edges), as in the methods described in [2,9,[12][13][14], or of (more commonly) (ii) merged edges with multiple origin or destination nodes (see Figure 2). Regarding the bundling methodologies, an edge bundling method can construct bundles in an explicit or in an implicit way [15].…”

“…(a) Divided Edge Bundling [6] (b) Stub Bundling [9] (c) SideKnot [9] (d) EEB with partial edges, α = 70 • . …”