Please complete these problems to the best of your ability and submit your solutions on Canvas by 11:59pm (EDT) on Saturday, July 1. There are (25) total points available in this problem set. 1. (PageRank) (20 points) The following graph depicts a small collection of webpages. Directed edges indicate hyperlinks from one site to the next. SocNetv PageRank 10 5 Figure 1: Collection of Webpages with Directed Hyperlinks (a) (5 points) A directed graph is said to be strongly connected if for every pair of nodes vi and vj, there is a directed path from v to v, and there is also a directed path from v, to v. Is this graph strongly connected? Briefly explain. (b) (5 points) Let's suppose that each node starts with a PageRank of. Write down the PageRank that each node will have after one update step. (c) (5 points) Write out the equations that describe the equilibrium (true) PageRank values. No need to solve them. (d) (5 points) Let's suppose that we removed the directed edge from node 10 to node 4, as well as the directed edge from node 10 to node 5. What would be the PageRank values of each node after a large number of updates? Briefly explain.