  Let $m_{ij}$ be the mean first passage time from state $i$ to state $j$ in an
$n$-state ergodic homogeneous Markov chain with transition matrix $T$. Let $G$
be the weighted digraph without loops whose vertex set coincides with the set
of states of the Markov chain and arc weights are equal to the corresponding
transition probabilities. We give a graph-theoretic interpretation to $m_{ij}$.
Namely, We show that $m_{ij}=f_{ij}/q_j$ if $i\ne j$ and $m_{ij}=1/\tilde q_j$
if $i=j$, where $f_{ij}$ is the total weight of 2-tree spanning converging
forests in $G$ that have one tree containing $i$ and the other tree converging
to $j$, $q_j$ is the total weight of spanning trees converging to $j$ in $G$,
and $\tilde q_j=q_j/\sum_{k=1}^nq_k$. The result is illustrated by an example.
  Keywords: Markov chain; Mean first passage time; Spanning rooted forest;
Matrix forest theorem; Laplacian matrix
