Maximum Flow Minimum Cut

[Yendall]

What is the best way to determine the maximum flow of a network diagram?
Is there a way of doing this without trial and error?

This constantly bugs me, there must be a way to figure this out with a formula or something.

[Hodgeyhodgey]

Last year I found that the majority of these questions can be solved simply by working top to bottom i.e. find the smallest no. on the top line, join it to the next smallest on the next line, etc.

Unfortunately there's no quick fix to solve these questions, some can be done immediately but others actually require a little bit of trial and error.

[Yendall]

Last year I found that the majority of these questions can be solved simply by working top to bottom i.e. find the smallest no. on the top line, join it to the next smallest on the next line, etc.

Unfortunately there's no quick fix to solve these questions, some can be done immediately but others actually require a little bit of trial and error.

Oh okay, I'll make sure I use the smallest first.
Can the maximum flow be found from either cutting flow from the sink or the source? Or is it just cutting the source?

[Hodgeyhodgey]

Either, because when you think about it if you cut it at the sink, that still stops the flow that has come from the source. If you get what I mean..

[Yendall]

Either, because when you think about it if you cut it at the sink, that still stops the flow that has come from the source. If you get what I mean..

Okay, yeah I understand what you mean. As long as the cut stops any flow from source to he sink it can be used. Is there any rule against how extreme a cut can be? Because they could go all over the network if need be?

[Hodgeyhodgey]

Either, because when you think about it if you cut it at the sink, that still stops the flow that has come from the source. If you get what I mean..

Okay, yeah I understand what you mean. As long as the cut stops any flow from source to he sink it can be used. Is there any rule against how extreme a cut can be? Because they could go all over the network if need be?

I'm not quite sure what you mean by 'extreme', but as long as the cut stops any flow from the source to the sink you're fine

[Yendall]

Either, because when you think about it if you cut it at the sink, that still stops the flow that has come from the source. If you get what I mean..

Okay, yeah I understand what you mean. As long as the cut stops any flow from source to he sink it can be used. Is there any rule against how extreme a cut can be? Because they could go all over the network if need be?

I'm not quite sure what you mean by 'extreme', but as long as the cut stops any flow from the source to the sink you're fine

"Extreme" as in "all over the place" haha, however that wouldn't be very beneficial as the flow would be enormous due to a mass amount of activities being cut. Thank you for your help, it clarified a few things, I appreciate it

[plato]

If you do  try a complicated (extreme?) cut, just remember that you must ignore any cut edge where the arrow indicates the flow would come from the sink side of the cut toward the source side. Only count the cut edges that flow from the source side toward the sink side.
This may seem confusing, especially if some edges appear to be drawn flowing from the right to the left on the diagram. You could try colouring in all of the diagram on the source side of a cut. All cut edges that flow from the uncoloured side into the coloured side of the cut can then be ignored.