notes there are bunch of junctions (nodes in the graphand bunch of pipes (edges in the graphconnecting the junction the pipe will only allow water to flow one way (the graph is directedeach pipe has also has capacity (the weight of the edge)representing the maximum amount of water that can flow through the pipe finallywe pour an infinite amount of water into the source vertex the problem is to find the maximum flow of the graph the maximum amount of water that will flow to the sink below is an example of network flow graph figure simple network flow graph there are currently no water flowing / / / / / it is fairly easy to see that the maximum flow in the figure is we can flow units of water from units of water from tand units of water from this gives flow of and since all incoming edge to the sink are saturatedthis is indeed the maximum flow note in the examplenot all pipe are saturated with water ford fulkerson method it was easy to see the solution in the above examplebut how do we find the solution in generalone idea is to keep finding path from to along pipes which still has some capacities remaining and push as much flow from to as possible we will then terminate once we can' find any more path this idea seem to work since it is exactly how we found the maximum flow in the example howeverthere is one problem we cannot guarantee which path we'll find first in factif we picked the wrong paththe whole algorithm will go wrong for examplewhat happens if lovely professional university