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Consider a toy small example of a directed web graph G = (V;E):(a) Suppose we assign all 18 nodes equal initial page rank values of 118 . Now supposewe apply the unscaled Page Rank algorithm to this graph. After one iteration (orround) of the algorithm, will any nodes have a page rank value of zero? If so, whichones and why? If not, briefly explain why not.(b) Answer the same question as in part (a) for both two and three iterations of unscaledpage rank.(c) When the algorithm converges (i.e., reaches equilibrium), which nodes in the graphwill have non-zero page rank values? What will their equilibrium page rank valuesbe? Briefly justify your answer.(d) Suppose we repeat part (a) but consider a variation of the graph in which a singlenode can delete a single one of their outgoing edges. Which nodes can increasetheir (equilibrium) page rank values by deleting a single outgoing edge? Brieflyjustify your answer. (Do not consider simultaneous deletion of multiple edges, justone single edge.)(e) What is the minimum number of edges that would need to be added to the graphso that every node has non-zero page rank? Briefly explain what edges would beneeded and why.(f) Suppose we use scaled Page Rank on the original graph in part (a) with scaling factors = 0:9. Which nodes will have non-zero (equilibrium) page rank values? Qualitatively,briefly describe which node will now have the highest page rank value.

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