# What is the Minimum Flow in a graph network (not the min cost flow problem)

Can anybody describe what the minimum flow in a graph network is please? I am not referring to the Minimum Cost Flow Problem here.

The minimum flow I believe is the opposite to the max flow of a network. The max flow seems intuitive in that you are trying to find the max flow through a network and you could use the min-cut approach.

But I cannot understand the minimum flow of a network. This is a paper that discuss the concept. I thought that the min flow of a network is 0 but obvious that has no value.

Paper

For a minimum flow problem, we take a network where each edge $$e$$ has an interval $$[l_e, u_e]$$ associated with it; the requirement for a feasible flow is (in addition to the flow condition) that the flow along $$e$$ must fall into this interval.
This is is a generalization of the networks usually used in the maximum flow problems, where the interval for an edge $$e$$ with capacity $$c_e$$ is $$[0, c_e]$$. However, if $$l_e > 0$$ for some edges, then the $$0$$ flow is not feasible, and so the minimum flow is not trivial to find.