Find the maximum flux path between two nodes
The problem is known as "Maximum capacity path problem" or  "Widest path problem"

See the original paper: T. C. Hu, "The Maximum Capacity Route Problem", Operations Research Vol. 9, No. 6 (Nov. - Dec., 1961), pp. 898-900

or the linear time algorithm described in: A. P. Punnen, "A linear time algorithm for the maximum capacity path problem" (but I didn't download/read it)