In Exercise 2, we considered how the consistuent parts of the bow-tie structure change as edges are added to or removed from the graph. It’s also interesting to ask about the magnitude of these changes.

(a) Describe an example of a graph where removing a single edge can reduce the size of the largest SCC by at least 1000 nodes. (Clearly you shouldn’t attempt to draw the full graph; rather, you can describe it in words, and also draw a schematic picture if it’s useful.)

(b) Describe an example of a graph where adding a single edge can reduce the size of the set OUT by at least 1000 nodes. (Again, you should describe the graph rather than actually drawing it.)

Exercise 2

As new links are created and old ones are removed among an existing set of Web pages, the pages move between different parts of the bow-tie structure.

(a) Name an edge you could add or delete from the graph in Figure 13.8 so as to increase the size of the largest SCC.

(b) Name an edge you could add or delete from the graph in Figure 13.8 so as to increase the size of the set IN.

(c) Name an edge you could add or delete from the graph in Figure 13.8 so as to increase the size of the set OUT.