The Kemeny Constant for Finite Homogeneous Ergodic Markov Chains
 M. Catral,
 S. J. Kirkland,
 M. Neumann,
 N.S. Sze
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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.
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 Title
 The Kemeny Constant for Finite Homogeneous Ergodic Markov Chains
 Journal

Journal of Scientific Computing
Volume 45, Issue 13 , pp 151166
 Cover Date
 20101001
 DOI
 10.1007/s1091501093821
 Print ISSN
 08857474
 Online ISSN
 15737691
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Nonnegative matrices
 Group inverses
 Directed graphs
 Markov chains
 Stationary distribution vectors
 Stochastic matrices
 Mean first passage times
 Industry Sectors
 Authors

 M. Catral ^{(1)}
 S. J. Kirkland ^{(2)}
 M. Neumann ^{(3)}
 N.S. Sze ^{(4)}
 Author Affiliations

 1. Department of Mathematics and Computer Science, Xavier University, 3800 Victory Parkway, Cincinnati, OH, 45207, USA
 2. Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland
 3. Department of Mathematics, University of Connecticut, Storrs, CT, 062693009, USA
 4. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China