1. Text problem 4.1.
2. Text problem 4.4.
3. Text problem 4.8.
4. Text problem 4.9. (Assume that the graph has no negative-weight cycles.)
5. Text problem 4.18.
6. Text problem 4.19.
7. Consider the digraph given by this graph where each line of the file indicates an edge. There are 77,360 nodes and 905,468 directed edges. What is the number of nodes in the largest SCC? What is the number of edges in the largest SCC? Include your code with your answer.
By the way, here's a rendering of the graph from above. You can see that
it's fairly tightly clustered (in other words, the shortest paths are not
very long). The graph was constructed from 77,360 users of the popular
SlashDot website; each user named other users as either Friend or Foe,
thereby creating a digraph.