Random Walk on an Edge-Weighted Graph. Consider a Markovchain Xn on the set of vertices S of a finite graph. Associated with each pairof vertices i and j there is a nonnegative weight wij , which is 0...

Random Walk on an Edge-Weighted Graph. Consider a Markovchain Xn on the set of vertices S of a finite graph. Associated with each pairof vertices i and j there is a nonnegative weight wij , which is 0 if (i, j) is not an edge; and the probability of a transition from i to j is directly proportiona