numbers are integers.

In [NA]{} problems, typical connectivity functions are as follows.

-   [*Edge-connectivity $\lambda_G(s,v)$*]{} is the maximum number of pairwise edge disjoint $sv$-paths in $G$.

-   [*Node-connectivity $\kappa_G(s,v)$*]{} is the maximum number of pairwise internally disjoint $sv$-paths in $G$.

-   [*$Q$-connectivity $\lambda_G^Q(s,v)$*]{} for given $Q \subseteq V$, is the maximum number of $sv$ paths no two of which have an edge or an internal node in $Q$ in common. Note that $Q$-connectivity reduces to edge-connectivity if $Q=\emptyset$, and to node-connectivity if $Q=V$; namely, $\lambda_G^\emptyset(s,v)=\lambda_G(s,v)$ and $\lambda_G^V(s,v)=\kappa_G(s,v)$.

The corresponding versions of [NA]{} are edge-connectivity [NA]{} when $f_{sv}(I)=\lambda_{G+I}(s,v)$, node-connectivity [NA]{} when $f_{sv}(I)=\kappa_{G+I}(s,v)$, and $Q$-connectivity [NA]{} when $f_{sv}(I)=\lambda^Q_{G+I}(s,v)$.

Most papers that considered [SL]{} problems defined $(S,v)$-edge-connectivity $\lambda_G(S,v)$ as the maximum number of pairwise edge-disjoint $(S,v)$-paths. On the other hand, several definitions were used for $(S,v)$-node-connectivity $\kappa(S,v)$; in most of these definitions, $\kappa(S,v)=\infty$ if $v \in S$. Here we suggest a definition that captures previous definitions as particular cases.

Note that $\lambda_G^Q(s,v)$ is the maximum $sv$-flow value, where edges and nodes in $Q$ have unit capacities, while the capacity of the nodes in $V \setminus Q$ is $\infty$. Hence the $Q$-connectivity function $\lambda_G^Q(s,v)$ is the max-flow/min-cut value function in $G$ with node-capacities in 