In the iterations of the maximal flow algorithm, the sum of the capacity/flow values of at each end of an arc is always equal to the sum of the original capacity values at each end of the arc.

Question

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The maximal flow algorithm maintains a flow that is feasible with respect to the capacity constraints. This means that the flow on each arc is always less than or equal to the capacity of the arc. The sum of the capacity/flow values at each end of an arc is equal to the sum of the original capacity values at each end of the arc because the flow is conserved.

In the Iterations of the Maximal Flow Algorithm, the Sum