Abstract not found

We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to concentric circles centered at the origin. Such constraints are typical, e.g., in the layout of social 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. Our approach is based on an extension of stress minimization with a weighting scheme that gradually imposes radial constraints on the intermediate layout during the majorization process, and thus is an attempt to preserve as much information about the graph structure as possible. 1

As a consequence of the rising interest in longitudinal social networks and their analysis, there is also an increasing demand for tools to visualize them. We argue that similar adaptations of state-of-the-art graph-drawing methods can be used to visualize longitudinal networks and the fit of actor-based models, the most prominent approach for analyzing such networks. The proposed methods are illustrated on a longitudinal network of acquaintanceship among university freshmen.

PrEd [Ber00] is a force-directed algorithm that improves the existing layout of a graph while preserving its edge crossing properties. The algorithm has a number of applications including: improving the layouts of planar graph drawing algorithms, interacting with a graph layout, and drawing Euler-like diagrams. The algorithm ensures that nodes do not cross edges during its execution. However, PrEd can be computationally expensive and overlyrestrictive in terms of node movement. In this paper, we introduce ImPrEd: an improved version of PrEd that overcomes some of its limitations and widens its range of applicability. ImPrEd also adds features such as flexible or crossable edges, allowing for greater control over the output. Flexible edges, in particular, can improve the distribution of graph elements and the angular resolution of the input graph. They can also be used to generate Euler diagrams with smooth boundaries. As flexible edges increase data set size, we experience an execution/drawing quality trade off. However, when flexible edges are not used, ImPrEd proves to be consistently faster than PrEd. Categories and Subject Descriptors (according to ACM CCS): G.2.2 [Discrete Mathematics]: Graph Theory—Graph Algorithms

Graph visualization has been widely used to understand and present both global structural and local adjacency information in relational datasets (e.g., transportation networks, citation networks, or social networks). Graphs with dense edges, however, are difficult to visualize because fast layout and good clarity are not always easily achieved. When the number of edges is large, edge bundling can be used to improve the clarity, but in many cases, the edges could be still too cluttered to permit correct interpretation of the relations between nodes. In this paper, we present an ambiguity-free edge-bundling method especially for improving local detailed view of a complex graph. Our method makes more efficient use of display space and supports detail-on-demand viewing through an interactive interface. We demonstrate the effectiveness of our method with a public coauthorship network data.

We describe a new technique for graph layout subject to constraints. Compared to previous techniques the proposed method is much faster and scalable to much larger graphs. For a graph with n nodes, m edges and c constraints it computes incremental layout in time O(nlogn + m + c) per iteration. Also, it supports a much more powerful class of constraint: inequalities or equalities over the Euclidean distance between nodes. We demonstrate the power of this technique by application to a number of diagramming conventions which previous constrained graph layout methods could not support. Further, the constraint-satisfaction method—inspired by recent work in position-based dynamics—is far simpler to implement than previous methods.