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If we have the following subgraph of a graph where I will just show 2 nodes please, where the capacity is 7 and 2 respectively:

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Now, if we have received flow at node 1 of value 5, then we will have:

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Problem: could you please explain why this will cause the capacity to be added to edge 2 and thus edge 2 will have now a capacity of $2+5 = 7$ given that we know a capacity of edge is supposed to be fixed if I understand it right and flow across edge should be less than the capacity of an edge please?

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    $\begingroup$ All the explanation is given in CLRS. Could you please specify what you did not understand from the text? $\endgroup$ Sep 23, 2021 at 10:52

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