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Graph TheoryMediumDirected Graphs and Network Flows

Directed Graphs and Network Flows · Medium problem

A network has arcs s→as\to a (capacity 66), s→bs\to b (capacity 44), a→ba\to b (capacity 22), a→ta\to t (capacity 55), b→tb\to t (capacity 55). Someone proposes the assignment f(s,a)=6f(s,a)=6, f(s,b)=4f(s,b)=4, f(a,b)=2f(a,b)=2, f(a,t)=3f(a,t)=3, f(b,t)=5f(b,t)=5. Every arc respects its capacity, but this is NOT a valid flow. By how many units does inflow exceed outflow at vertex aa?