# Does Max Flow produce uniform results? [closed]

I am interested in using Max Flow algorithm. I want to simulate transfer of quantity. Anyway, I am unsure of some thing.

Does Max Flow algorithm produce uniformly distributed max flow?

I have provided example picture to show what I meant.

Black: edge capabilities Red: wrong, non-uniform results Green: correct, uniform results

max-flow-image-example

I do realize there are many types of Max Flow algorithms, so to add onto question, or to be more specific - which Max Flow algorithms produce uniform max flow and which don't?

Extra thing: I will use floating points (converted into integers) and then back. But I don't think this matters here.

## closed as unclear what you're asking by Dima Pasechnik, j.c., RP_, Mark Wildon, Neil HoffmanNov 26 '18 at 15:15

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• Uniformly in what sense? Different edges may have different capacities. – Dima Pasechnik Nov 22 '18 at 15:22
• Good point. I drew another picture. Lets say this way: uniform, if nothing is maxed out. If some edge is maxed out, then remaining quantity gets distributed equally to other non-maxed edges. Example picture: imgur.com/a/gZpRka2 I do not have "maxed out edge" scenario, but I shall draw some too. – Vili Volcini Nov 22 '18 at 15:53
• One path maxed out example pic: imgur.com/a/U9cDDXz – Vili Volcini Nov 22 '18 at 15:56
• It is a property of the problem that often the maximum is only reached on a path (with the edges outside it carrying no flow at all). That is, it's as non-uniform as it possibly could be. – Dima Pasechnik Nov 22 '18 at 16:10
• Many algorithms will always produce a basic solution (in the linear programming sense), thus an extreme point of the feasible region. This is, as Dima said, "as non-uniform as it possibly could be". – Robert Israel Nov 22 '18 at 16:24