Let ‘M denote the node-node adjacency matrix of a network G. Define ‘Mk = ‘M . ‘M k- I for each k…

Let 'M denote the node-node adjacency matrix of a network G. Define 'Mk = 'M . 'M k- I for each k = 2, 3, … , n. Show that the {ith entry of th~ matrix 'M2 is the number of directed paths consisting of two arcs from node ito nodej. Then using induction, show that the {ith entry of matrix 'Mk is the number of distinct walks from node i to node j containing exactly k arcs. In making this assessment, assume that two walks are distinct if their sequences of arcs are different (even if the unordered set of arcs are the same).

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