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Is FindMaximumFlow function broken?

I ran the example on FindMaximumFlow in the documentation and got the following results.

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My guess is that the answer is wrong. Instead of pairing with Billy, Mary can easily connect to Dustin and Alecia can then pair with Billy. When I run the results in Table to get maximum flows value I get 3 or 4. Am I wrong or is there something strange with the FindMaximumFlow function?
POSTED BY: Ali Hashmi
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POSTED BY: Szabolcs Horvát
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