Edge concentration: a method for clustering directed graphs

The display of a directed graph is a commonly used visual aid for representing relationships. However, some graphs contain so many edges that their display by traditional graph layout algorithms is virtually impossible because of the overwhelming number of crossings. Graphs representing large software systems and their configurations are particularly prone to this problem. Examples of such graphs include: graphs depicting a system's configuration, call graphs, graphs depicting import and export relationships between modules, and graphs depicting the “includes” relation among a system's source files. This paper proposes the elimination of some edges by replacing sets of edges that have the same set of source and target nodes by a special node called an edge concentration node. Reducing the number of edges often has the desirable side effect of reducing the number of crossings. An algorithm that determines a reasonable set of edge concentrations of a graph in &Ogr;(n4) operations for each level in the graph is presented where n is the number of nodes in that level. Several examples from the area of software configuration management are shown to demonstrate the effectiveness of using edge concentrations.