More Flexible Radial Layout

Abstract

Abstract. We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to the circumferences of a set of concentric circles around the origin. Such constraints frequently occur in the layout of social or policy networks, when structural centrality is mapped to geometric centrality, or when the primary intention of the layout is the display of the vicinity of a distinguished node. We extend stress majorization by a weighting scheme which imposes radial constraints on the layout but also tries to preserve as much information about the graph structure as possible.

Exploring Complex Drawings via Edge Stratification

“…We tested the whole set of force-directed algorithms available in the OGDF library: Kamada-Kawai (KK) [21], Fruchterman-Reingold(FR) [17], GEM (GEM) [16], FM 3 (FMMM) [19], and Stress majorization (SM) [4]. Since tuning is a critical issue for force-directed techniques, it is worth remarking that we initialized the algorithms by using the default parameters set by their implementations in the library.…”

“…. , 1000} we generated 10 graphs with density in the interval [4,8]. UserStudyGraphs, which contains the 5 graphs used in the user study.…”

Planar Preprocessing for Spring Embedders

“…(1) SpringEmbedderFR (FR) implements the force-directed layout algorithm by Fruchterman-Reingold [7] using a grid-variant of the algorithm to speed up the computation of repulsive forces (using the defaults: (i) 400 iterations, (ii) has small initial random perturbations, (iii) minimum distance of 20 between connected components, and (iv) automatic scaling), (2) SpringEmbedderFRExact (FRE) provides an alternative implementation of the FR spring embedder with exact force computations (using the defaults: (i) 1000 iterations, (ii) has small initial random perturbations, (iii) minimum distance of 20 between connected components, (iv) cooling factor of .9, (v) ideal edge length of 10, and (v) tolerance factor of 0.01, which the fraction of ideal length below which convergence is achieved); (3) SpringEmbedderKK (KK) implements that MDS spring embedder of Kamada and Kawai [10] (using the defaults: (i) stop tolerance of 0.0001 for energy level, (ii) maximum number of iterations is based on input graph, (iii) all edges have equal length, and (iv) desirable edge length is proportional to the area of the display grid divided by the maximum distance between two nodes in initial layout); and (4) StressMajorization (SM) implements simple stress majorization by Pich [3] that allows radial constraints based on shortest path distances (using the defaults: (i) 50 iterations and (ii) automatic scaling).…”

Large scale cohesive subgraphs discovery for social network visual analysis

“…the probability that the vertex degree in this k-mutual-friend subgraph is larger than d. Based on this nice property, the filtering operation on the hierarchy is reasonable without losing much structural information. Note that users can perceive more insights using orbital layout comparing with other popular layout algorithms, such as the radial layout [4] and the force directed layout [11]. Although radial layout is a hierarchical structure, it is sensitive to the focused vertex in the center and the layout may totally change with a different center.…”