What Graphs can be Efficiently Represented by BDDs?

We have carried out experimental research into implicit representation of large graphs using reduced ordered binary decision diagrams (OBDDs). We experimentally show that for graphs from real applications such as graphs representing the networks of the Internet or the World Wide Web and other technical and social networks the sizes of the corresponding OBDDs do not differ much from the number of edges which the graphs contain. It is noteworthy that all of these large graphs are sparse. For randomly generated dense graphs, the gain, i.e., the ratio of the number of graph edges to the OBDD size, increases with the number of vertices and the density of the graphs. The importance to know whether a graph falls into the region where algorithms based on OBDDs are more efficient than that based on adjacent lists and matrices is therefore emphasized through the results of this paper