Radial Coordinate Assignment for Level Graphs

A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information

“…The author would like to thank Michael Forster for contributing to the parent papers [15], [34] and Matthias Hö llmü ller for expunging some bugs and implementing his algorithms in Gravisto [33] within a network analysis package.…”

“…This paper is organized as follows: After some preliminary definitions in the next section, we present a complete framework in Sugiyama style to create radial level drawings of hierarchical graphs. This is done by introducing methods for radial level assignment in Section 3, radial crossing reduction in Section 4, and radial coordinate assignment [15] in Section 5. We omit the cycle removal step since it does not differ from the horizontal case and standard algorithms can be used.…”

Radial drawings of graphs: Geometric constraints and trade-offs

“…The algorithm computes the drawing by adding at each step a vertex and all its incident edges according to an ordering introduced by de Fraysseix, Pach and Pollack and known as a canonical ordering [8]. We remark here that for the case of radial layered graphs with monotone edges, an algorithm that computes a radial drawing with at most two bends per edge is given in [3]. The addition of v i to Γ i−1 at Step i is computed as follows.…”

“…On the other hand, the problem of computing radial drawings of planar graphs with no edge intersections and no bends along the edges has been studied in [10], but the described drawing algorithm does not take into account any semantic requirements. The problem of testing whether a graph admits a crossing-free radial drawing that satisfies the assigned centrality of the vertices and where the edges are monotone Jordan curves has been studied by Bachmaier et al [1,2]; if the test is positive, a planar embedding is provided; an algorithm for turning such an embedding into a drawing with at most two bends per edge is described in [3].…”

Radial Level Planarity Testing and Embedding in Linear Time

“…Now the vertices are placed on k concentric circles l j = { (j cos θ, j sin θ) | θ ∈ [0, 2π) }, 1 ≤ j ≤ k. A k-level graph is radial k-level planar if there are permutations of the vertices on each radial level such that the edges can be drawn as strictly monotone curves from inner to outer levels without crossings. Such drawings [3] extend the radial tree drawings of Eades [16], where the levels of the vertices are given by their depth, i. e., BFS-level. Figure 1(b) shows a radial level planar drawing of the graph in Figure 1(a) which is not level planar.…”