The maximum flow between vertices 
and 
in a graph 
is exactly the weight of the smallest set of edges to disconnect
with 
and 
in different components (Ford and Fulkerson 1962; Skiena 1990, p. 178).
Maximum Flow, Minimum Cut Theorem
See also
Network FlowExplore with Wolfram|Alpha
References
Ford, L. R. and Fulkerson, D. R. Flows in Networks. Princeton, NJ: Princeton University Press, 1962.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Referenced on Wolfram|Alpha
Maximum Flow, Minimum Cut TheoremCite this as:
Weisstein, Eric W. "Maximum Flow, Minimum Cut Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MaximumFlowMinimumCutTheorem.html