how to find overall min-cut separating some node pairs, not all node pairs

xyw2013

As we know, now there is efficient algorithms to find the overall min-cut in a directed graph, e.g. Hao and Orlin (1994).
9 y  K7 d) i" L8 X
4 e  y1 i. ^% V. W1 nNow my problem is to find an overall min-cut just separating some given node pairs, not all the node pairs. For example, I have an 8-node digraph with capacities on each arc and want to find the overall min-cut separating some node pairs such as 8 and 1, 6 and 3, 7 and 1. The algorithm of Hao and Orlin (1994) cannot solve my problem.
& h! @$ c$ o3 u
! U" O* f" A7 }, P4 \$ N
# {- K6 _. V/ S+ t* Y9 E不好意思，我用英文至少为了把问题说的更清楚一点