Drawing Large Graphs with a Potential-Field-Based Multilevel Algorithm

A new force-directed graph drawing method that is based on a combination of an efficient multilevel scheme and a strategy for approximating the repulsive forces in the system by rapidly evaluating potential fields is presented.

Abstract

Force-directed graph drawing algorithms are widely used for drawing general graphs. However, these methods do not guarantee a sub-quadratic running time in general. We present a new force-directed method that is based on a combination of an efficient multilevel scheme and a strategy for approximating the repulsive forces in the system by rapidly evaluating potential fields. Given a graph G=(V,E), the asymptotic worst case running time of this method is O(|V|\\log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs containing 100000 nodes in less than 5 minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for some other methods.