A 1-separation formula for the graph Kemeny constant and Braess edges

The Kemeny constant of a Markov chain

Given an ergodic finite-state Markov chain, let Miw denote the mean time from i to equilibrium, meaning the expected time, starting from i, to arrive at a state selected randomly according to the equilibrium measure w of the chain. John Kemeny observed that Miw does not depend on starting the point i. The common value K = Miw is the Kemeny constant or seek time of the chain. K is a spectral inv...

The Maximum Number of Edges in a Strongly Multiplicative Graph

The Kemeny Constant for Finite Homogeneous Ergodic Markov Chains

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

the maximum number of edges in a strongly multiplicative graph

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Kemeny's Constant And An Analogue Of Braess' Paradox For Trees

Given an irreducible stochastic matrix M, Kemeny’s constant K(M) measures the expected time for the corresponding Markov chain to transition from any given initial state to a randomly chosen final state. A combinatorially based expression for K(M) is provided in terms of the weights of certain directed forests in a directed graph associated with M , yielding a particularly simple expression in ...