Define
$$ A = \left( \begin{matrix} .5 & .5 \\ .5 & .5 \end{matrix} \right),\; \; B = \left( \begin{matrix} .99 & .01 \\ .01 & .99 \end{matrix} \right), \; \; C = \left( \begin{matrix} .01 & .99 \\ .99 & .01 \end{matrix} \right)$$

Taken as Markov chains, clearly $A$ permits movement between its states better than $B$, and $C$ permits movement between its states better than $A$. 

Is there some sort of measure on the space of Markov chains that measures how well they permit movement between their states? Some kind of congestion or accessibility statistic? 

Edit: I know about mixing rates, but I'm wondering about a statistic that works for absorbing Markov chains too.