Let $D = (V,A)$ be a finite directed graph, and let $T \subseteq V$. Call a subset $I \subseteq V$ linkable to $T$ if there exists a family $(P_i)_{i \in I}$ of pairwise vertex-disjoint directed paths in $D$ such that, for each $i \in I$, the path $P_i$ starts at $i$ and ends at a vertex of $T$, and the endpoints in $T$ are distinct. Paths of length zero are allowed, so a vertex $i \in I \cap T$ may be linked to itself.

Then the family

\begin{align*} \mathcal I = \{I \subseteq V : I \text{ is linkable to } T\} \end{align*}

is the collection of independent sets of a matroid on the ground set $V$.