• 19.1 Find a large digraph somewhere online—perhaps a transaction graph in some online system, or a digraph defined by links on Web pages.

• 19.2 Find a large DAG somewhere online—perhaps one defined by class-definition dependencies in a large software system, or by directory links in a large file system.

Make a table like Screenshot, but exclude from the counts graphs and digraphs with self-loops.

How many digraphs are there that contain V vertices and E edges?

19.5 How many digraphs correspond to each undirected graph that contains V vertices and E edges?

19.6 How many digits do we need to express the number of digraphs that have V vertices as a base-10 number?

19.7 Draw the nonisomorphic digraphs that contain three vertices.

••• 19.8 How many different digraphs are there with V vertices and E edges if we consider two digraphs to be different only if they are not isomorphic?

19.9 Compute an upper bound on the percentage of 10-vertex digraphs that could ever be examined by any computer, under the assumptions described in the text and the additional ones that the universe has less than 10^{80} electrons and that the age of the universe will be less than 10^{20} years.