we mention some node-connectivity functions $\psi$ that appear in the literature, and show that they are particular case of the $(p,q)$-connectivity function $\lambda_G^{p,q}$ with $p_u,q_u \in \{1,\infty\}$ and $q_u \leq p_u$.

1.  $\kappa(S,v)$ is the maximum number of $(S,v)$-paths no two of which have a common node in $V \setminus (S \cup v)$ if $v \notin S$, and $\kappa(S,v)=\infty$ otherwise; equivalently, $\kappa(S,v)$ is the minimum size $|C|$ of a cut $C \subseteq E \cup V \setminus (S \cup \{v\})$ such that $G \setminus C$ has no $(S,v)$-path.\
    For directed graphs, [$\kappa$-SL]{} is equivalent to [$\lambda$-SL]{} by the following (approximation ratio preserving) standard reduction: replace every $v \in V$ by two nodes $v^{in}, v^{out}$ connected by an edge $v^{in}v^{out}$, and replace every edge $uv \in E$ by an edge $u^{out}v^{in}$; each node $v^{out}$ inherits the cost and the demand of $v$, while $v^{in}$ has cost $\infty$ and demand $0$. It is not hard to verify that $S$ is a feasible solution to the original instance with connectivity function $\kappa$ if, and only if, $S^{out}=\{v^{out}:v \in S\}$ is a feasible solution to the obtained instance with the edge-connectivity function $\lambda$. For undirected graphs, we do not see that $\kappa$ is a particular 