CiSE: A Circular Spring Embedder Layout Algorithm

We present a new algorithm for automatic layout of clustered graphs using a circular style. The algorithm tries to determine optimal location and orientation of individual clusters intrinsically within a modified spring embedder. Heuristics such as reversal of the order of nodes in a cluster and swap of neighboring node pairs in the same cluster are employed intermittently to further relax the spring embedder system, resulting in reduced inter-cluster edge crossings. Unlike other algorithms generating circular drawings, our algorithm does not require the quotient graph to be acyclic, nor does it sacrifice the edge crossing number of individual clusters to improve respective positioning of the clusters. Moreover, it reduces the total area required by a cluster by using the space inside the associated circle. Experimental results show that the execution time and quality of the produced drawings with respect to commonly accepted layout criteria are quite satisfactory, surpassing previous algorithms. The algorithm has also been successfully implemented and made publicly available as part of a compound and clustered graph editing and layout tool named CHISIO.