I found this problem in the Mining of Massive Datasets textbook by Jeff Ullman. I tried solving it by doing it recursively, but it seems my answer is wrong. Is there a solution to this problem where the page rank of the root node is 0.5, and it successively reduces after each level of the binary tree.
The graph is attached below:
Repeat Exercise 5.1.6 for the tree of dead ends suggested by Fig. 5.10. That is, there is a single node with a self-loop, which is also the root of a complete binary tree of n levels.
For context: Excercise 5.1.6: Suppose we recursively eliminate dead ends from the graph, solve the remaining graph, and estimate the PageRank for the dead-end pages as described in Section 5.1.4. Suppose the graph is a chain of dead ends, headed by a node with a self-loop, as suggested in Fig. 5.9. What would be the PageRank assigned to each of the nodes?