I'm attempting to build a network with maximum flow using weights 1-18 such that the loss of an individual node (not the source or sink) causes the least disruption to the flow.
I know that the max-flow min-cut theorem states that in any network, the value of any maximum flow is equal to the capacity of any minimum cut. With the out-degree of the source and in-degree of the sink to be maximized, I believe I'd want some combination of 18,13,14 coming out of $a$ and 12,17,16 into $j$, showing a capacity of 45.
However, from there I'm not sure. Any thoughts/directions?