Matrix analysis
The Group Inverse Associated with an Irreducible Periodic Nonnegative Matrix
SIAM Journal on Matrix Analysis and Applications
A Matrix Perturbation View of the Small World Phenomenon
SIAM Journal on Matrix Analysis and Applications
Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation
SIAM Journal on Matrix Analysis and Applications
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A quantity known as the Kemeny constant, which is used to measure the expected number of links that a surfer on the World Wide Web, located on a random web page, needs to follow before reaching his/her desired location, coincides with the more well known notion of the expected time to mixing, i.e., to reaching stationarity of an ergodic Markov chain. In this paper we present a new formula for the Kemeny constant and we develop several perturbation results for the constant, including conditions under which it is a convex function. Finally, for chains whose transition matrix has a certain directed graph structure we show that the Kemeny constant is dependent only on the common length of the cycles and the total number of vertices and not on the specific transition probabilities of the chain.