#### CSCI 3104 - Algorithms - Spring 2011

### Problem Set #7

#### Due: 12pm, Mar 9th, 2011

1. Text problem 4.18.

2. Text problem 4.19.

3. 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.

4. Using the same graph you used in number 4, find the diameter of the graph.
(The diameter of a graph is the max of all shortest paths in the graph;
this means you'll have to find the shortest path from every vertex to every
other.) I intend to talk about techniques for implementing this, in class,
before it's due. Be sure and include your code with your solution.

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.