\to \{1 {, \dots ,} n\}
\setminus I$ (a permutation of $k = n-s$ points).

Geometrically $G$ is a union of disjoint directed cycles passing through all vertices except $i_1 {, \dots ,} i_s$.

\[Ex:Forest\] Let $n > k$; then any graph $G \in \Gamma_{n,k}$ contains at least $n-k$ connected components. If $G$ is acyclic then every its connected component contains a sink. So for $I = \{i_1 {, \dots ,} i_s\}$ if $\AC_{n,k}^I \ne
{\varnothing}$ then $k \ge n-s$.

Let $k = n-s$. Then the elements of $\AC_{n,k}^I$ are forests of $s$ components, each component containing exactly one vertex $i_\ell \in I$ (for some $\ell = 1 {, \dots ,} s$), which is its only sink. This component is a tree and every its edge is directed towards the sink $i_\ell$.

Determinants and minors
-----------------------

Let $W = (w_{ij})$ be a $n \times n$-matrix; denote by $\langle W \vert:
\Graph_{n,k} \to \Complex$ a linear functional acting on the basic element $G \in \Gamma_{n,k}$ as $$\langle W \mid G\rangle {\stackrel{\mbox{\scriptsize def}}{=}}\prod_{[ij] \in G} w_{ij}.$$ Note that $\langle W \mid G\rangle$ is independent of the edge numbering in $G$; in particular, $\langle W \mid G_1*G_2 - G_2*G_1\rangle = 0$ for all 