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Let $p$ be a real number greater than one and let $\Gamma$ be a graph ofbounded 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 $p$-harmonicboundary of $\Gamma$ consists of at least $n$ elements. We also show that theconverse of this statement is also true.

The $p$-harmonic boundary and $D_p$-massive subsets of a graph of bounded degree