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Unformatted text preview: degree of vertex k, d(k), is the number of edges that terminate at vertex k. Four examples of connected graphs with no self-loops are shown below. Let G be a finite connected graph with no self-loops. A random walk on G starts at a given vertex, and at each time step it moves to one of its neighbors. All its neighbors are chosen with equal probability. a) Explain how this random walk can be represented as a finite Markov chain. Determine the transition probabilities P ij in terms of the interconnectivity of the graph. b) Find the steady-state probabilities ur for this random walk. Is the Markov chain reversible? 3) Problem 6.7 from the course notes. 4) Problem 6.11 from the course notes. 5) Problem 6.16 from the course notes....
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