Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Graph drawing by force-directed placement
Software—Practice & Experience
A multilevel algorithm for partitioning graphs
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
Drawing graphs nicely using simulated annealing
ACM Transactions on Graphics (TOG)
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
JIGGLE: Java Interactive Graph Layout Environment
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Multilevel Visualization of Clustered Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
A Fast Multi-Scale Method for Drawing Large Graphs
A Fast Multi-Scale Method for Drawing Large Graphs
A Multi-Scale Algorithm for Drawing Graphs Nicely
A Multi-Scale Algorithm for Drawing Graphs Nicely
InterViewer: Dynamic Visualization of Protein-Protein Interactions
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Graph Drawing by High-Dimensional Embedding
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Smashing Peacocks Further: Drawing Quasi-Trees from Biconnected Components
IEEE Transactions on Visualization and Computer Graphics
Topographic Visualization of Prefix Propagation in the Internet
IEEE Transactions on Visualization and Computer Graphics
Rapid Multipole Graph Drawing on the GPU
Graph Drawing
The Binary Stress Model for Graph Drawing
Graph Drawing
Graph visualization with latent variable models
Proceedings of the Eighth Workshop on Mining and Learning with Graphs
An experimental comparison of fast algorithms for drawing general large graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Energy-based clustering of graphs with nonuniform degrees
GD'05 Proceedings of the 13th international conference on Graph Drawing
Graph drawing by stress majorization
GD'04 Proceedings of the 12th international conference on Graph Drawing
Drawing large graphs with a potential-field-based multilevel algorithm
GD'04 Proceedings of the 12th international conference on Graph Drawing
Visualizing large graphs with compound-fisheye views and treemaps
GD'04 Proceedings of the 12th international conference on Graph Drawing
Visualisation and analysis of large and complex scale-free networks
EUROVIS'05 Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization
Graph drawing by subspace optimization
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
A scalable parallel force-directed graph layout algorithm
EG PGV'08 Proceedings of the 8th Eurographics conference on Parallel Graphics and Visualization
ISMIS'12 Proceedings of the 20th international conference on Foundations of Intelligent Systems
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We describe a heuristic method for drawing graphs which uses a multilevel technique combined with a force-directed placement algorithm. The multilevel process groups vertices to form clusters, uses the clusters to define a new graph and is repeated until the graph size falls below some threshold. The coarsest graph is then given an initial layout and the layout is successively refined on all the graphs starting with the coarsest and ending with the original. In this way the multilevel algorithm both accelerates and gives a more global quality to the force-directed placement. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on a number of examples ranging from 500 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 30 seconds for a 10,000 vertex graph to around 10 minutes for the largest graph. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.