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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 selfloops are shown below. Let G be a finite connected graph with no selfloops. 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 steadystate 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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This note was uploaded on 10/21/2010 for the course EE 5581 taught by Professor Moon,j during the Spring '08 term at Minnesota.
 Spring '08
 Moon,J
 Computer Science, Electrical Engineering

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