# A Multilevel Algorithm for Force-Directed Graph Drawing

**C. Walshaw**

**April 20, 2000**

### Abstract:

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 optimised 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 100,000 vertices.
It is also very fast and can compute a layout in around 30 seconds for a 10,000 vertex graph to around 10-20 minutes for the larger graphs.

**Keywords:**
Graph drawing, multilevel, force directed placement.

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Fri Aug 13 13:39:56 BST 2004