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

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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) 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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Problem 1 Compute the PageRank vector of the network for a 1 normalized such that the sum of the centralities over all nodes is equal to one Solution ... View the full answer