  Let $p$ be a real number greater than one and let $\Gamma$ be a graph of
bounded degree. We investigate links between the $p$-harmonic boundary of
$\Gamma$ and the $D_p$-massive subsets of $\Gamma$. In particular, if there are
$n$ pairwise disjoint $D_p$-massive subsets of $\Gamma$, then the $p$-harmonic
boundary of $\Gamma$ consists of at least $n$ elements. We also show that the
converse of this statement is also true.
