An algorithm for drawing general undirected graphs
Information Processing Letters
Graph drawing by force-directed placement
Software—Practice & Experience
Drawing graphs in the plane with high resolution
SIAM Journal on Computing
Drawing graphs nicely using simulated annealing
ACM Transactions on Graphics (TOG)
A force-directed algorithm that preserves edge-crossing properties
Information Processing Letters - Special issue analytical theory of fuzzy control with applications
Spring algorithms and symmetry
Theoretical Computer Science - computing and combinatorics
A Fast Adaptive Layout Algorithm for Undirected Graphs
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
A multi-dimensional approach to force-directed layouts of large graphs
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
Non-Euclidean Spring Embedders
IEEE Transactions on Visualization and Computer Graphics
Visual Exploration of Complex Time-Varying Graphs
IEEE Transactions on Visualization and Computer Graphics
Multi-Level Graph Layout on the GPU
IEEE Transactions on Visualization and Computer Graphics
MOVIS: A system for visualizing distributed mobile object environments
Journal of Visual Languages and Computing
IEEE Transactions on Visualization and Computer Graphics
Drawing graphs with nonuniform nodes using potential fields
Journal of Visual Languages and Computing
Automatic visualisation of metro maps
Journal of Visual Languages and Computing
Drawing large graphs with a potential-field-based multilevel algorithm
GD'04 Proceedings of the 12th international conference on Graph Drawing
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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The conventional force-directed methods for drawing undirected graphs are based on either vertex-vertex repulsion or vertex-edge repulsion. In this paper, we propose a new force-directed method based on edge-edge repulsion to draw graphs. In our framework, edges are modelled as charged springs, and a final drawing can be generated by adjusting positions of vertices according to spring forces and the repulsive forces, derived from potential fields, among edges. Different from the previous methods, our new framework has the advantage of overcoming the problem of zero angular resolution, guaranteeing the absence of any overlapping of edges incident to the common vertex. Given graph layouts probably generated by previous algorithms as the inputs to our algorithm, experimental results reveal that our approach produces promising drawings not only preserving the original properties of a high degree of symmetry and uniform edge length, but also preventing zero angular resolution and usually having larger average angular resolution. However, it should be noted that exhibiting a higher degree of symmetry and larger average angular resolution does not come without a price, as the new approach might result in the increase in undesirable overlapping of vertices as some of our experimental results indicate. To ease the problem of node overlapping, we also consider a hybrid approach which takes into account both edge-edge and vertex-vertex repulsive forces in drawing a graph.