Consider a network composed of four web pages. Suppose page 1 has a link to pages 2 and 3. Suppose page 3 has a link to page 4. Suppose page 4 has a link to page 3.

1. Draw a graph to represent this network. Identify any dead-end nodes.

2. Draw a modified graph with artificial edges from dead-end nodes to every node in the graph, as required by the PageRank algorithm.

3. Present the system of PageRank equations for nodes 1 and 2 on the modified graph drawn previously. Let α denote the probability of teleportation.