Question: 1. Consider the network given in the figure below where each edge has weight one. Compute the PageRank vector of the network, for a

1. Consider the network given in the figure below where each edge has weight one. Compute the PageRank vector

1. Consider the network given in the figure below where each edge has weight one. Compute the PageRank vector of the network, for a over all nodes is equal to one. = 1, normalized such that the sum of the centralities 3 2 (1p) 2. Does the value of the PageRank vector align with your intuition? Why? [Hint: think of the interpretation in terms of random walks] (1p) 3. An undirected graph is said to be regular if all nodes have the same degree. Show that the PageRank vector of a regular graph of size n (normalized to sum to one) is 1/n (for all values of a), where n is the number of nodes. (1p)

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