A flow network is a set of pipes with capacities running from a source to a sink. A cut is any way of splitting the nodes into a source side and a sink side; its capacity is the total of the pipes crossing forward, from the source side to the sink side. Every unit of oil that reaches the terminal must cross every cut, so no flow can beat the smallest cut, and the max-flow min-cut theorem says the maximum flow is exactly equal to that minimum cut. Here the tank can release 24, but only 23 ever arrives, because the two pipes into the terminal add to 23. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.
A network is a diagram that turns a real system — roads, pipes, cables, schedules — into dots and weighted lines, and every question is about optimising one thing along those lines. Either you connect everything for the least total cost (spanning tree) or you push the most through a fixed structure (flow). The bottleneck is always the answer.
Oil flows from a tank through five pipes to a terminal while a dashed amber line shows one of the four source–sink cuts and sums its forward pipes, so a flow of 23 can be matched against cuts of 24, 25, 26 and 23.
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