A Fast Multi-level Algorithm for Drawing Large Undirected Graphs

Graph drawing is a standard means for visualizing the relational information. This paper presents a fast algorithm for drawing large undirected graphs with straight-line edges, which employs the multi-level method as the framework of the algorithm and adopts the force-directed algorithm combined with bary-centralizing method to refine the single-level layouts. As far as we know, it is the first attempt to introduce this kind of combination. Also, the other two speed-up methods, constraint-normalization and quad-tree space decomposition, are used. Systematic experiments suggest its high performance and nice results. It is extremely fast and can nicely draw 10,000 vertex graphs in approximately 5 seconds and 1000,000 vertex graphs in approximately 11 minutes. The comparison with the well-known algorithms proves its validity and practicality. Furthermore, the presented algorithm is easy to implement, and its techniques can be generalized to speed up general force-directed algorithms.