Minimizing the Number of Edges via Edge Concentration in Dense Layered Graphs.
Edge concentration in dense bipartite graphs is a technique for reducing the numbers of edges and edge crossings in graph drawings. The conventional method proposed by Newbery is designed to reduce the number of edge crossings; however, it does not always reduce the number of edges. Reducing the number of edges is also an important factor for improving the readability of graphs. However, no edge concentration method with the explicit purpose of minimizing the number of edges has previously been studied. In this study, we propose a novel, efficient heuristic method for minimizing the number of edges during edge concentration. We demonstrate the efficiency of the proposed method via a comparison using randomly generated graphs. We find that Newbery's method fails to reduce the number of edges when the number of vertices is large. By contrast, the proposed method achieves an average compression ratio of 47 to 82 percent for all generated graph groups. We also present a real-world application of the proposed method using a causality network of biological data.